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Longer titles found: Non-Archimedean geometry (view), Non-Archimedean ordered field (view), Non-Archimedean time (view)

searching for Non-Archimedean 123 found (189 total)

Local field (1,670 words) [view diff] exact match in snippet view article find links to article

In mathematics, a field K is called a (non-Archimedean) local field if it is complete with respect to a topology induced by a discrete valuation v and

Ultrametric space (1,581 words) [view diff] exact match in snippet view article find links to article

{\displaystyle z} . Sometimes the associated metric is also called a non-Archimedean metric or super-metric. An ultrametric on a set M is a real-valued

Absolute value (algebra) (1,317 words) [view diff] exact match in snippet view article

|x + y| ≤ max(|x|, |y|) for all x and y, then |x| is called an ultrametric or non-Archimedean absolute value, and otherwise an Archimedean absolute value. If |x|1

Nth-term test (693 words) [view diff] case mismatch in snippet view article find links to article

is a necessary and sufficient condition for convergence due to the non-archimedean triangle inequality. Unlike stronger convergence tests, the term test

Dehn plane (640 words) [view diff] exact match in snippet view article find links to article

of the angles of a triangle is less than π. Dehn's examples use a non-Archimedean field, so that the Archimedean axiom is violated. They were introduced

Algebraic number field (8,365 words) [view diff] exact match in snippet view article find links to article

x\in K} . The second and third classes are Archimedean places and non-Archimedean (or ultrametric) places. The completion of K {\displaystyle K} with

Iwasawa decomposition (905 words) [view diff] exact match in snippet view article find links to article

NM^{T}=MN^{T}\right\}.} There is an analog to the above Iwasawa decomposition for a non-Archimedean field F{\displaystyle F}: In this case, the group GLn(F){\displaystyle

Restricted power series (1,376 words) [view diff] case mismatch in snippet view article find links to article

whose coefficients approach zero as degree goes to infinity. Over a non-archimedean complete field, the ring is also called a Tate algebra. Quotient rings

Otto Stolz (386 words) [view diff] exact match in snippet view article find links to article

Ehrlich (2006). "The rise of non-Archimedean mathematics and the roots of a misconception. I. The emergence of non-Archimedean systems of magnitudes", Archive

Berkovich space (1,544 words) [view diff] exact match in snippet view article find links to article

introduced by Berkovich (1990), is a version of an analytic space over a non-Archimedean field (e.g. p-adic field), refining Tate's notion of a rigid analytic

Local Tate duality (565 words) [view diff] case mismatch in snippet view article find links to article

is a duality for Galois modules for the absolute Galois group of a non-archimedean local field. It is named after John Tate who first proved it. It shows

Unipotent representation (374 words) [view diff] case mismatch in snippet view article find links to article

and θ10. Lusztig (1995) classified the unipotent characters over non-archimedean local fields. Vogan (1987) discusses several different possible definitions

Krasner's lemma (531 words) [view diff] case mismatch in snippet view article find links to article

relating the topology of a complete non-archimedean field to its algebraic extensions. Let K be a complete non-archimedean field and let K be a separable closure

Local Euler characteristic formula (478 words) [view diff] case mismatch in snippet view article find links to article

cohomology of the absolute Galois group GK of a non-archimedean local field K. Let K be a non-archimedean local field, let Ks denote a separable closure

Completion of a ring (1,581 words) [view diff] exact match in snippet view article find links to article

sequences, and agrees with it in the case when R has a metric given by a non-Archimedean absolute value. Suppose that E is an abelian group with a descending

Quasi-finite field (478 words) [view diff] case mismatch in snippet view article find links to article

deals with complete valued fields whose residue field is finite (i.e. non-archimedean local fields), but the theory applies equally well when the residue

Langlands group (243 words) [view diff] case mismatch in snippet view article find links to article

F is local archimedean, LF is the Weil group of F, when F is local non-archimedean, LF is the product of the Weil group of F with SU(2). When F is global

Pseudo-differential operator (1,402 words) [view diff] exact match in snippet view article find links to article

models that include ultrametric pseudo-differential equations in a non-Archimedean space. The study of pseudo-differential operators began in the mid

Finite extensions of local fields (371 words) [view diff] case mismatch in snippet view article find links to article

tools such as ramification groups. In this article, a local field is non-archimedean and has finite residue field. Let L / K {\displaystyle L/K} be a finite

Banach algebra (2,602 words) [view diff] exact match in snippet view article find links to article

algebra A {\displaystyle A} over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space

Sébastien Boucksom (630 words) [view diff] exact match in snippet view article find links to article

introduced by Boucksom and collaborators Berman and Jonsson using non-Archimedean geometry to study Kähler manifolds have been very influential in the

Invariant subspace problem (2,163 words) [view diff] exact match in snippet view article find links to article

a non-Archimedean field admits a bounded linear operator without a non-trivial closed invariant subspace. This completely solves the non-Archimedean version

Kirillov model (397 words) [view diff] exact match in snippet view article find links to article

functions on the local field. If G is the algebraic group GL2 and F is a non-Archimedean local field, and τ is a fixed nontrivial character of the additive

P-adic valuation (1,103 words) [view diff] exact match in snippet view article find links to article

| p {\displaystyle |r+s|_{p}\leq |r|_{p}+|s|_{p}} follows from the non-Archimedean triangle inequality | r + s | p ≤ max ( | r | p , | s | p ) {\displaystyle

Tate–Shafarevich group (1,381 words) [view diff] no match in snippet view article find links to article

obtained from K by completing with respect to all its Archimedean and non Archimedean valuations v). Thus, in terms of Galois cohomology, Ш(A/K) can be defined

Giuseppe Veronese (359 words) [view diff] exact match in snippet view article find links to article

continuity which was the foundation for his development of the first non-Archimedean linear continuum. Veronese produced several significant monographs

Tropical geometry (3,506 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \operatorname {Trop} (X)} is the non-Archimedean amoeba over an algebraically closed non-Archimedean field K. If X is a variety over C {\displaystyle

Hasse norm theorem (500 words) [view diff] case mismatch in snippet view article find links to article

is a statement about completions in all valuations, archimedean and non-archimedean. The theorem is no longer true in general if the extension is abelian

Nicole De Grande-De Kimpe (552 words) [view diff] exact match in snippet view article find links to article

work on locally convex topological vector spaces over fields with non-Archimedean valuations. De Grande-De Kimpe was born on 7 September 1936 in Antwerp

Bogomolov conjecture (416 words) [view diff] exact match in snippet view article find links to article

Xander (eds.). Tropical and non-Archimedean geometry. Bellairs workshop in number theory, tropical and non-Archimedean geometry, Bellairs Research Institute

Transfer principle (2,700 words) [view diff] exact match in snippet view article find links to article

handled correctly. For example, since the hyperreal numbers form a non-Archimedean ordered field and the reals form an Archimedean ordered field, the

Reinhardt Kiehl (354 words) [view diff] case mismatch in snippet view article find links to article

emeritus. His research deals with algebraic and arithmetic geometry and non-archimedean function theory. He wrote with Eberhard Freitag a textbook on the Weil

Ring of integers (1,054 words) [view diff] case mismatch in snippet view article find links to article

a set of fundamental units. One defines the ring of integers of a non-archimedean local field F as the set of all elements of F with absolute value ≤ 1;

Schwartz–Bruhat function (1,550 words) [view diff] case mismatch in snippet view article find links to article

^{n}} , while for the non-archimedean places the f v {\displaystyle f_{v}} are the Schwartz–Bruhat functions of non-archimedean local fields.) The space

Infinitesimal (5,092 words) [view diff] exact match in snippet view article find links to article

Ehrlich, P. (2006) The rise of non-Archimedean mathematics and the roots of a misconception. I. The emergence of non-Archimedean systems of magnitudes. Arch

Disphenocingulum (354 words) [view diff] exact match in snippet view article find links to article

Zbl 0132.14603. Timofeenko, A. V. (2009-10-17). "The non-platonic and non-Archimedean noncomposite polyhedra". Journal of Mathematical Sciences. 162 (5):

The Principles of Mathematics (1,873 words) [view diff] exact match in snippet view article find links to article

Philip (2006), "The rise of non-Archimedean mathematics and the roots of a misconception. I. The emergence of non-Archimedean systems of magnitudes", Archive

Pregeometry (physics) (1,150 words) [view diff] exact match in snippet view article

of space-time. Number theory pregeometry by Volovich Spacetime as a non-Archimedean geometry over a field of rational numbers and a finite Galois field

Snub square antiprism (557 words) [view diff] exact match in snippet view article find links to article

Ways. 46 (3): 177. Timofeenko, A. V. (2009). "The non-Platonic and non-Archimedean noncomposite polyhedra". Journal of Mathematical Science. 162 (5):

Rigid analytic space (985 words) [view diff] exact match in snippet view article find links to article

cohomology Non-Archimedean analysis by S. Bosch, U. Güntzer, R. Remmert ISBN 3-540-12546-9 Brian Conrad Several approaches to non-archimedean geometry lecture

Takagi existence theorem (827 words) [view diff] case mismatch in snippet view article find links to article

modulus m is a product of a non-archimedean (finite) part mf and an archimedean (infinite) part m∞. The non-archimedean part mf is a nonzero ideal in

Sphenocorona (576 words) [view diff] exact match in snippet view article find links to article

S2CID 122006114, Zbl 0132.14603 Timofeenko, A. V. (2009), "The non-Platonic and non-Archimedean noncomposite polyhedra", Journal of Mathematical Science, 162 (5):

Pythagorean field (1,044 words) [view diff] case mismatch in snippet view article find links to article

satisfy Hilbert's completeness axiom. The Pythagorean closure of a non-archimedean ordered field, such as the Pythagorean closure of the field of rational

Arithmetization of analysis (334 words) [view diff] exact match in snippet view article find links to article

analysis by Abraham Robinson in the 1960s, whereas in reality the work on non-Archimedean systems continued unabated, as documented by P. Ehrlich; the shift

Class formation (2,670 words) [view diff] case mismatch in snippet view article find links to article

formal Laurent series over a finite field, and G is the Galois group. Non-archimedean local class field theory of characteristic 0: The module A is the group

Weierstrass preparation theorem (1,218 words) [view diff] case mismatch in snippet view article find links to article

for }}\nu _{1}+\dots +\nu _{n}\to \infty \right\}} over a complete non-archimedean field k. These algebras are the basic building blocks of rigid geometry

Sphenomegacorona (584 words) [view diff] exact match in snippet view article find links to article

S2CID 122006114, Zbl 0132.14603. Timofeenko, A. V. (2009), "The non-Platonic and non-Archimedean noncomposite polyhedra", Journal of Mathematical Science, 162 (5):

Hebesphenomegacorona (504 words) [view diff] exact match in snippet view article find links to article

Zbl 0132.14603. Timofeenko, A. V. (2009-10-17). "The non-platonic and non-Archimedean noncomposite polyhedra". Journal of Mathematical Sciences. 162 (5):

Hà Huy Khoái (656 words) [view diff] exact match in snippet view article find links to article

work has been p-adic Nevanlinna theory, for example proving part of a non-Archimedean version of Green's theorem (AMS, 1992, 503-509). He has been the Vietnam

Hecke algebra of a locally compact group (405 words) [view diff] case mismatch in snippet view article find links to article

when G is a group of points of a reductive algebraic group over a non-archimedean local field F, such as Qp, and K is what is now called an Iwahori subgroup

Strassmann's theorem (213 words) [view diff] exact match in snippet view article find links to article

was introduced by Reinhold Straßmann (1928). Let K be a field with a non-Archimedean absolute value | · | and let R be the valuation ring of K. Let f(x)

Tate topology (80 words) [view diff] exact match in snippet view article find links to article

admissible open coverings. Conrad, Brian (2008), "Several approaches to non-Archimedean geometry", in Thakur, Dinesh S.; Savitt, David (eds.), p-adic geometry

Bernstein–Zelevinsky classification (186 words) [view diff] exact match in snippet view article find links to article

(1976), "Representations of the group GL(n,F), where F is a local non-Archimedean field" (PDF), Akademiya Nauk SSSR I Moskovskoe Matematicheskoe Obshchestvo

Vojta's conjecture (592 words) [view diff] case mismatch in snippet view article find links to article

F(P)/F{\displaystyle F(P)/F}. There are generalizations in which the non-archimedean local heights λD,v{\displaystyle \lambda _{D,v}} are replaced by truncated

Building (mathematics) (3,170 words) [view diff] exact match in snippet view article

from certain groups, namely, reductive algebraic groups over a local non-Archimedean field. Furthermore, if the split rank of the group is at least three

Brauer group (2,943 words) [view diff] exact match in snippet view article find links to article

R), the class of H has order two in the Brauer group. Let K be a non-Archimedean local field, meaning that K is complete under a discrete valuation

Vladimir Gennadievich Sprindzuk (755 words) [view diff] case mismatch in snippet view article find links to article

effective approximations to algebraic numbers both in archimedean and non-archimedean domains. Sprindzuk's results are based on the connections between linear

Stanley Tennenbaum (118 words) [view diff] case mismatch in snippet view article find links to article

memory of Stanley Tennenbaum". mamls.org. Stanley Tennenbaum (1959). "Non-archimedean models for arithmetic". Notices of the American Mathematical Society

Triangular hebesphenorotunda (667 words) [view diff] exact match in snippet view article find links to article

S2CID 122006114, Zbl 0132.14603. Timofeenko, A. V. (2009). "The non-Platonic and non-Archimedean noncomposite polyhedra". Journal of Mathematical Science. 162 (5):

Henry Forder (460 words) [view diff] no match in snippet view article find links to article

pages are devoted to "concepts of classes, relations, linear order, non archimedean systems, ..." and that order axioms together with a continuity axiom

Satake isomorphism (861 words) [view diff] exact match in snippet view article find links to article

{\displaystyle G} be a semisimple algebraic group, K {\displaystyle K} be a non-Archimedean local field and O {\displaystyle O} be its ring of integers. It's easy

Emmanuel Ullmo (230 words) [view diff] case mismatch in snippet view article find links to article

Kazuhiko Yamaki, "Survey on the geometric Bogomolov conjecture", talk at "Non-archimedean analytic Geometry: Theory and Practice" (Papeete, 24–28 August 2015)

Identity component (869 words) [view diff] exact match in snippet view article find links to article

matrices of negative determinant. Any connected algebraic group over a non-Archimedean local field K is totally disconnected in the K-topology and thus has

Jacobson ring (829 words) [view diff] case mismatch in snippet view article find links to article

algebra over an uncountable field is a Jacobson ring. Tate algebras over non-archimedean fields are Jacobson rings. A commutative ring R is a Jacobson ring

Steinberg symbol (632 words) [view diff] exact match in snippet view article find links to article

trivial symbol. The characterisation of weakly continuous symbols on a non-Archimedean local field F was obtained by Moore. The group K2(F) is the direct

Hasse invariant of an algebra (768 words) [view diff] exact match in snippet view article find links to article

representing each class by some element of Br(L/K) as above. For a non-Archimedean local field, the invariant map is a group isomorphism. In the case

Langlands–Shahidi method (1,542 words) [view diff] case mismatch in snippet view article find links to article

root numbers when v gives an archimedean local field or when v is non-archimedean and πv{\displaystyle \pi _{v}} is a constituent of an unramified principal

Tennenbaum's theorem (1,057 words) [view diff] exact match in snippet view article find links to article

in Logic. Vol. 36. ISBN 9781107008045. Tennenbaum, Stanley (1959). "Non-Archimedean models for arithmetic". Notices of the American Mathematical Society

Ordered exponential field (784 words) [view diff] exact match in snippet view article find links to article

} does not have the Archimedean property, this is an example of a non-Archimedean ordered exponential field. The ordered field of logarithmic-exponential

Mirabolic group (342 words) [view diff] exact match in snippet view article find links to article

GL(N) and the classification of unitary representations of GL(N) (non-Archimedean case)", Lie group representations, II (College Park, Md., 1982/1983)

Michael Rapoport (537 words) [view diff] exact match in snippet view article find links to article

2011 Heinz Hopf Prize. In 1994, he was an Invited Speaker (with talk Non-Archimedean period domains) at the ICM in Zürich. Rapoport's students include Maria

Conductor (class field theory) (1,227 words) [view diff] case mismatch in snippet view article

related to the Artin map. Let L/K be a finite abelian extension of non-archimedean local fields. The conductor of L/K, denoted f ( L / K ) {\displaystyle

Yan Soibelman (221 words) [view diff] case mismatch in snippet view article find links to article

direct construction of Calabi-Yau varieties based on SYZ conjecture and non-archimedean geometry, and more recently to Donaldson-Thomas theory. Together with

Nagata ring (642 words) [view diff] exact match in snippet view article find links to article

Society of Japan, 3rd Series, 17: 327–336 Bosch, Güntzer, Remmert, Non-Archimedean Analysis, Springer 1984, ISBN 0-387-12546-9 Danilov, V.I. (2001) [1994]

Real tree (1,593 words) [view diff] case mismatch in snippet view article find links to article

Kharlampovich, A. Myasnikov, D. Serbin, Actions, length functions and non-archimedean words IJAC 23, No. 2, 2013.{{citation}}: CS1 maint: multiple names:

Weil group (983 words) [view diff] case mismatch in snippet view article find links to article

Weil–Deligne group scheme (or simply Weil–Deligne group) W′K of a non-archimedean local field, K, is an extension of the Weil group WK by a one-dimensional

Galois module (1,920 words) [view diff] case mismatch in snippet view article find links to article

Kudla, Stephen S. (1994), "The local Langlands correspondence: the non-archimedean case", Motives, Part 2, Proc. Sympos. Pure Math., vol. 55, Providence

Snub disphenoid (1,877 words) [view diff] exact match in snippet view article find links to article

ISBN 9780387986500. Timofeenko, A. V. (2009), "The non-Platonic and non-Archimedean noncomposite polyhedra", Journal of Mathematical Science, 162 (5):

Infinitary logic (1,736 words) [view diff] case mismatch in snippet view article find links to article

suitable infinitary logic. Other examples include the theories of non-archimedean fields and torsion-free groups.[better source needed] These three theories

Absolute value (3,299 words) [view diff] exact match in snippet view article find links to article

which satisfies any (hence all) of the above conditions is said to be non-Archimedean, otherwise it is said to be Archimedean. Again the fundamental properties

Gelfand pair (3,964 words) [view diff] case mismatch in snippet view article find links to article

usual notion of admissible representation when the local field is non-archimedean. When the local field is archimedean, admissible representation instead

Vladimir Berkovich (165 words) [view diff] exact match in snippet view article find links to article

Berkovich, Vladimir G. (1990), Spectral theory and analytic geometry over non-Archimedean fields, Mathematical Surveys and Monographs, vol. 33, Providence, R

Newton polygon (2,257 words) [view diff] case mismatch in snippet view article find links to article

behaviour of the roots. Let K{\displaystyle K} be a field endowed with a non-archimedean valuation vK:K→R∪{∞}{\displaystyle v_{K}:K\to \mathbb {R} \cup \{\infty

Generalised metric (894 words) [view diff] exact match in snippet view article find links to article

the trick is done without choice. Case II: F {\displaystyle F} is a non-Archimedean field. For given x ∈ G {\displaystyle x\in G} where G {\displaystyle

Johannes de Groot (1,028 words) [view diff] exact match in snippet view article find links to article

research include a proof that a metrizable topological space has a non-Archimedean metric (satisfying the strong triangle inequality d(x,z) ≤ max(d(x

Height function (1,910 words) [view diff] exact match in snippet view article find links to article

Fubini–Study metrics on the Archimedean fields and the usual metric on the non-Archimedean fields. It is the usual Weil height equipped with a different metric

Linearly ordered group (1,398 words) [view diff] exact match in snippet view article find links to article

group isomorphisms. Completing a l.o. group can be difficult in the non-Archimedean case. In these cases, one may classify a group by its rank: which is

Degeneration (algebraic geometry) (596 words) [view diff] exact match in snippet view article

toric degenerations M. Kontsevich, Y. Soibelman: Affine structures and non-Archimedean analytic spaces, in: The unity of mathematics (P. Etingof, V. Retakh

Tate curve (1,068 words) [view diff] exact match in snippet view article find links to article

ISBN 0-387-94328-5. Zbl 0911.14015. Tate, John (1995) [1959], "A review of non-Archimedean elliptic functions", in Coates, John; Yau, Shing-Tung (eds.), Elliptic

Norbert Schappacher (967 words) [view diff] exact match in snippet view article find links to article

nichtarchimedischen Körpern (A diophantine invariant of singularities over non-Archimedean fields). He was from 1979 to 1981 at Paris-Sud University (University

Negative probability (2,460 words) [view diff] exact match in snippet view article find links to article

235–248. ISBN 978-0415069601. Khrennikov, Andrei Y. (March 7, 2013). Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models

David Soudry (436 words) [view diff] exact match in snippet view article find links to article

Epsilon Factors for Generic Representations of GSp(4,k)xGL(2,k) over a Local Non-Archimedean Field k (1983) Doctoral advisor Ilya Piatetski-Shapiro

Abelian sandpile model (4,878 words) [view diff] exact match in snippet view article find links to article

Xander (eds.). Tropical and non-Archimedean geometry. Bellairs workshop in number theory, tropical and non-Archimedean geometry, Bellairs Research Institute

Georg Cantor (9,976 words) [view diff] exact match in snippet view article find links to article

P. (2006). "The rise of non-Archimedean mathematics and the roots of a misconception. I. The emergence of non-Archimedean systems of magnitudes" (PDF)

Johnson solid (1,743 words) [view diff] exact match in snippet view article find links to article

Further Convex polyhedra Timofeenko, A.V. (2009). "The Non-Platonic and Non-Archimedean Noncomposite Polyhedra". J. Math. Sci. 162 (5): 710–729. doi:10

Fake projective plane (1,480 words) [view diff] exact match in snippet view article find links to article

Masa-Nori; Kato, Fumiharu (1998), "The strong rigidity theorem for non-Archimedean uniformization", The Tohoku Mathematical Journal, Second Series, 50

Alexei Gvishiani (1,846 words) [view diff] exact match in snippet view article find links to article

representations for the group of matrices with elements from a local non-Archimedean field (1973–74). During his university studies he was influenced by

Graduate Studies in Mathematics (4,466 words) [view diff] exact match in snippet view article find links to article

Equations, Walter Craig (2018, ISBN 978-1-4704-4292-7) 198 Dynamics in One Non-Archimedean Variable, Robert L Benedetto (2019, ISBN 978-1-4704-4688-8) 199 Applied

A. H. Lightstone (1,330 words) [view diff] exact match in snippet view article find links to article

Lightstone, who himself died soon after. It begins with an introduction to non-Archimedean fields with many helpful examples, brings in the necessary tools from

Local Langlands conjectures (2,041 words) [view diff] exact match in snippet view article find links to article

Kudla, Stephen S. (1994), "The local Langlands correspondence: the non-Archimedean case", in Jannsen, Uwe; Kleiman, Steven; Serre, Jean-Pierre (eds.)

Compact space (5,681 words) [view diff] exact match in snippet view article find links to article

maximal ideals m in C(X) such that the residue field C(X)/m is a (non-Archimedean) hyperreal field. The framework of non-standard analysis allows for

Algebraic number theory (5,798 words) [view diff] exact match in snippet view article find links to article

field. If the valuation is Archimedean, one obtains R or C, if it is non-Archimedean and lies over a prime p of the rationals, one obtains a finite extension

Siegfried Bosch (290 words) [view diff] exact match in snippet view article find links to article

OCLC 851822593. Bosch, Siegfried; Güntzer, Ulrich; Remmert, Reinhold (1984). Non-Archimedean analysis a systematic approach to rigid analytic geometry. Berlin.

Friedwardt Winterberg (2,925 words) [view diff] exact match in snippet view article find links to article

2002). The Planck Aether Hypothesis: An Attempt for a Finitistic Non-Archimedean Theory of Elementary Particles. C.F. Gauss Academy of Science Press

Iwahori–Hecke algebra (2,051 words) [view diff] case mismatch in snippet view article find links to article

when G is a group of points of a reductive algebraic group over a non-archimedean local field K, such as Qp, and K is what is now called an Iwahori subgroup

Riesz space (5,296 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {R} ^{2}} with the lexicographical order is a non-Archimedean Riesz space. Riesz spaces are lattice ordered groups Every Riesz space

Field (mathematics) (10,335 words) [view diff] exact match in snippet view article

bound. Any complete field is necessarily Archimedean, since in any non-Archimedean field there is neither a greatest infinitesimal nor a least positive

Aubrey William Ingleton (762 words) [view diff] exact match in snippet view article find links to article

the literature as Ingleton's inequality. ‘Hahn–Banach theorem for non-Archimedean-valued fields’. Proc. Cambridge Philos. Soc. 48 (1) (1952) 41–45. ‘The

Hyperreal number (4,892 words) [view diff] exact match in snippet view article find links to article

others, infinitesimals were largely abandoned, though research in non-Archimedean fields continued (Ehrlich 2006). However, in the 1960s Abraham Robinson

Seminorm (6,139 words) [view diff] exact match in snippet view article find links to article

for the usual norm discussed in this article. An ultraseminorm or a non-Archimedean seminorm is a seminorm p : X → R {\displaystyle p:X\to \mathbb {R}

Riemann zeta function (10,291 words) [view diff] exact match in snippet view article find links to article

factors in the Euler product expansion being the local L-factors of the non-Archimedean places. The functional equation shows that the Riemann zeta function

Azumaya algebra (3,007 words) [view diff] case mismatch in snippet view article find links to article

colimit is taken over all finite Galois field extensions. Over a local non-archimedean field F{\displaystyle F}, such as the p-adic numbers Qp{\displaystyle

Wieferich prime (6,935 words) [view diff] case mismatch in snippet view article find links to article

variable over a finite field and let E be an elliptic curve. If v is a non-archimedean place of norm qv of K and a ∈ K, with v(a) = 0 then v(aqv − 1 − 1)

Congruence subgroup (4,778 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \mathbb {A} _{f}} are the restricted product of all non-archimedean completions (all p-adic fields). If Γ ⊂ G ( Q ) {\displaystyle \Gamma

0.999... (13,418 words) [view diff] exact match in snippet view article find links to article

structures, including various alternatives to the real numbers, which are non-Archimedean. Non-standard analysis provides a number system with a full array of

Glossary of arithmetic and diophantine geometry (4,745 words) [view diff] exact match in snippet view article find links to article

Fubini–Study metrics on the Archimedean fields and the usual metric on the non-Archimedean fields. Arakelov theory Arakelov theory is an approach to arithmetic

Foundations of geometry (10,876 words) [view diff] exact match in snippet view article find links to article

examples of geometries satisfying all except the Archimedean axiom V.1 (non-Archimedean geometries), all except the parallel axiom IV.1 (non-Euclidean geometries)

Christopher Deninger (3,515 words) [view diff] exact match in snippet view article find links to article

Here p is either a prime number or infinity, corresponding to the non-Archimedean Euler factors and the Archimedean Euler factor respectively, and Rp

Algebraic K-theory (10,382 words) [view diff] exact match in snippet view article find links to article

followed Gauss's first proof of the Law of Quadratic Reciprocity. For non-Archimedean local fields, the group K2(F) is the direct sum of a finite cyclic

Bass–Serre theory (5,830 words) [view diff] case mismatch in snippet view article find links to article

useful in the study of discrete subgroups of algebraic groups over non-archimedean local fields and in the study of Kac–Moody groups. Development of foldings

Adele ring (18,454 words) [view diff] exact match in snippet view article find links to article

denoting the uniformising element by π v . {\displaystyle \pi _{v}.} A non-Archimedean valuation is written as v < ∞ {\displaystyle v<\infty } or v ∤ ∞ {\displaystyle

List of women in mathematics (22,165 words) [view diff] exact match in snippet view article find links to article

Annette Werner (born 1966), German expert on diophantine geometry and non-Archimedean algebraic geometry Elisabeth M. Werner, researcher on convex geometry

Index of philosophy articles (I–Q) (12,368 words) [view diff] case mismatch in snippet view article

Nominalization Nomological danglers Nomos Nomothetic Nomothetic and idiographic Non-archimedean time Non-Aristotelian logic Non-classical logic Non-cognitivism Non-essentialism