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Longer titles found: Dual abelian variety (view), Semistable abelian variety (view), Conductor of an abelian variety (view)

searching for Abelian variety 20 found (254 total)

alternate case: abelian variety

Supersingular variety (318 words) [view diff] exact match in snippet view article find links to article

ring of endomorphisms of rank 4. Supersingular Abelian variety Sometimes defined to be an abelian variety isogenous to a product of supersingular elliptic

Riemann form (262 words) [view diff] exact match in snippet view article find links to article

form. Furthermore, the complex torus Cg/Λ admits the structure of an abelian variety if and only if there exists an alternating bilinear form α such that

Torsion conjecture (1,393 words) [view diff] exact match in snippet view article find links to article

abelian varieties states that the order of the torsion group of an abelian variety over a number field can be bounded in terms of the dimension of the

Schottky problem (862 words) [view diff] exact match in snippet view article find links to article

on which an abelian variety depends, then the Schottky problem asks simply what condition on the parameters implies that the abelian variety comes from

Serre–Tate theorem (153 words) [view diff] exact match in snippet view article find links to article

This was first proved by Jean-Pierre Serre when the reduction of the abelian variety is ordinary, using the Greenberg functor; then John Tate gave a proof

Albanese variety (989 words) [view diff] exact match in snippet view article find links to article

generalization of the Jacobian variety of a curve. The Albanese variety is the abelian variety A {\displaystyle A} generated by a variety V {\displaystyle V} taking

CM-field (718 words) [view diff] exact match in snippet view article find links to article

the quotient by its center is the group Gal(QR/Q). If V is a complex abelian variety of dimension n, then any abelian algebra F of endomorphisms of V has

Fano surface (742 words) [view diff] exact match in snippet view article find links to article

of two curves and are not a complete intersection of divisors in an Abelian variety. The Fano surface S of a smooth cubic threefold F into P4 carries many

Selmer group (607 words) [view diff] exact match in snippet view article find links to article

constructed from an isogeny of abelian varieties. The Selmer group of an abelian variety A with respect to an isogeny f : A → B of abelian varieties can be

List of algebraic number theory topics (187 words) [view diff] exact match in snippet view article find links to article

Euler system p-adic L-function Arithmetic geometry Complex multiplication Abelian variety of CM-type Chowla–Selberg formula Hasse–Weil zeta function

Chowla–Selberg formula (505 words) [view diff] exact match in snippet view article find links to article

complex multiplication, and in particular in the theory of periods of an abelian variety of CM-type. This has led to much research and generalization. In particular

Arithmetic dynamics (1,665 words) [view diff] exact match in snippet view article find links to article

integer points on a variety Rational and integer points in an orbit Points of finite order on an abelian variety Preperiodic points of a rational function

Ramanujam–Samuel theorem (226 words) [view diff] exact match in snippet view article find links to article

3101–3103, MR 0154887 Seshadri, C. S. (1963), "Quotient space by an abelian variety", Mathematische Annalen, 152: 185–194, doi:10.1007/BF01470879, ISSN 0025-5831

James Milne (mathematician) (463 words) [view diff] exact match in snippet view article

1994 Milne, James S. (1968). "The Tate-Šafarevič group of a constant abelian variety". Inventiones Mathematicae. 6: 91–105. Bibcode:1968InMat...6...91M

Artin conductor (935 words) [view diff] exact match in snippet view article find links to article

representations are used to defined the conductor of an elliptic curve or abelian variety. Serre (1967) p.158 Serre (1967) p.159 Manin, Yu. I.; Panchishkin,

Marvin Greenberg (437 words) [view diff] case mismatch in snippet view article find links to article

thesis Pro-Algebraic Structure on the Rational Subgroup of a P-Adic Abelian Variety. From 1955 Greenberg was an assistant at Princeton, from 1958 an assistant

Marvin Greenberg (437 words) [view diff] case mismatch in snippet view article find links to article

thesis Pro-Algebraic Structure on the Rational Subgroup of a P-Adic Abelian Variety. From 1955 Greenberg was an assistant at Princeton, from 1958 an assistant

Moduli of abelian varieties (761 words) [view diff] exact match in snippet view article find links to article

\mathbb {C} ^{2g}} . Fixing such a basis removes the automorphisms of an abelian variety at a point in the moduli space, hence there exists a bona-fide algebraic

Supersingular K3 surface (1,401 words) [view diff] exact match in snippet view article find links to article

In particular, this gives the standard notion of a supersingular abelian variety. For a variety X over a finite field Fq, it is equivalent to say that

Tautological ring (1,649 words) [view diff] exact match in snippet view article find links to article

{\mathcal {M}}_{g,1}} , by Yin. Powers of theta-divisor on the universal abelian variety, by Grushevsky and Zakharov. These four methods are proven to give