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Syntomic topology
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Mazur defined a morphism to be syntomic if it is flat and locally a complete intersection. The syntomic topology is generated by surjective syntomic morphismsAtiyah–Hirzebruch spectral sequence (1,971 words) [view diff] exact match in snippet view article find links to article
\mathbb {Z} /2\to 0} Consider a smooth complete intersection 3-fold X {\displaystyle X} (such as a complete intersection Calabi-Yau 3-fold). If we look atCotangent complex (4,731 words) [view diff] exact match in snippet view article find links to article
smoothable complete intersection morphism, this complex is perfect. Furthermore, if g : Y → Z is another smoothable complete intersection morphism andMiles Reid (331 words) [view diff] case mismatch in snippet view article find links to article
Institutions Christ's College, Cambridge University of Warwick Thesis The Complete Intersection of Two or More Quadratics (1972) Doctoral advisor Peter Swinnerton-DyerFano surface (742 words) [view diff] exact match in snippet view article find links to article
type that are not related to a product of two curves and are not a complete intersection of divisors in an Abelian variety. The Fano surface S of a smoothConifold (865 words) [view diff] exact match in snippet view article find links to article
Philip; Dale, A.M.; Lutken, Andrew; Schimmrigk, Rolf (1988), "Complete intersection Calabi-Yau manifolds", Nuclear Physics B, 298 (3): 493–525, Bibcode:1988NuPhBRiemann–Roch-type theorem (663 words) [view diff] exact match in snippet view article find links to article
Also, if f : X → Y {\displaystyle f:X\to Y} is a (global) local complete intersection morphism; i.e., it factors as a closed regular embedding X ↪ P {\displaystyleMatrix factorization (algebra) (610 words) [view diff] case mismatch in snippet view article
Triangulated category Eisenbud, David (1980). "Homological Algebra on a Complete Intersection, with an Application to Group Respresentations" (PDF). TransactionsIntegrally closed domain (1,924 words) [view diff] exact match in snippet view article find links to article
satisfies (ii). Geometrically, we have the following: if X is a local complete intersection in a nonsingular variety; e.g., X itself is nonsingular, then XDerived scheme (2,276 words) [view diff] exact match in snippet view article find links to article
{\displaystyle d} is the usual universal derivation. If we take a complete intersection, then the koszul complex R ∙ = C [ x 1 , … , x n ] ( f 1 ) ⊗ C [Analytic space (1,031 words) [view diff] exact match in snippet view article find links to article
singular locus has codimension at least two. When X is a local complete intersection at x, then X is normal at x. Non-normal analytic spaces can be smoothedRosa M. Miró-Roig (350 words) [view diff] case mismatch in snippet view article find links to article
(Birkhäuser 2007) and co-authored the monograph Gorenstein Liaison, Complete Intersection Liaison Invariants and Unobstructedness (American Mathematical SocietyMircea Mustață (566 words) [view diff] exact match in snippet view article find links to article
Lawrence; Mustaţǎ, Mircea (2004). "Inversion of adjunction for local complete intersection varieties". American Journal of Mathematics. 126 (6): 1355–1365Hans-Bjørn Foxby (77 words) [view diff] exact match in snippet view article find links to article
Alzheimer's disease on 8 April 2014. Sather-Wagstaff, Keri Ann. "Complete intersection dimensions and Foxby classes" (PDF). Journal of Pure and AppliedMatrix factorization of a polynomial (196 words) [view diff] exact match in snippet view article find links to article
Eisenbud, David (1980-01-01). "Homological algebra on a complete intersection, with an application to group representations". Transactions ofSupport of a module (904 words) [view diff] exact match in snippet view article find links to article
{\displaystyle f_{1},f_{2}\in R} in an integral domain which form a complete intersection ideal ( f 1 , f 2 ) {\displaystyle (f_{1},f_{2})} , the tensor propertyPerfect obstruction theory (596 words) [view diff] exact match in snippet view article find links to article
^{n}]} In particular, if Y {\displaystyle Y} is a smooth local complete intersection then the perfect obstruction theory is the cotangent complex (whichReal algebraic geometry (3,217 words) [view diff] exact match in snippet view article find links to article
algebraic subset of R n {\displaystyle \mathbb {R} ^{n}} which is a complete intersection (from the conclusion of this theorem the word "component" can notPerverse sheaf (2,253 words) [view diff] exact match in snippet view article find links to article
system F {\displaystyle {\mathcal {F}}} . If X is a flat, locally complete intersection (for example, regular) scheme over a henselian discrete valuationLeray spectral sequence (2,448 words) [view diff] exact match in snippet view article find links to article
examples can be computed if Y is simply connected; for example a complete intersection of dimension ≥ 2 {\displaystyle \geq 2} (this is because of theDualizing sheaf (1,018 words) [view diff] exact match in snippet view article find links to article
with open restrictions. Example: If f {\displaystyle f} is a local complete intersection morphism between schemes of finite type over a field, then (by definition)Coherent sheaf (6,934 words) [view diff] exact match in snippet view article find links to article
{\displaystyle V(s)} is a codimension 2 subvariety, then It is a local complete intersection, meaning if we take an affine chart U i ⊆ X {\displaystyle U_{i}\subseteqSatoshi Suzuki (mathematician) (799 words) [view diff] exact match in snippet view article
torsion of the module of differentials of a locality which is a complete intersection, 1965, cited by 15 including one textbook Homologie des algèbresHochschild homology (3,399 words) [view diff] exact match in snippet view article find links to article
Hochschild homology not just for smooth algebras, but also for local complete intersection algebras. In this case, given a presentation A = R / I {\displaystyleCone (algebraic geometry) (1,354 words) [view diff] exact match in snippet view article
embedding of the normal cone into the normal bundle. Consider the complete intersection ideal ( f , g 1 , g 2 , g 3 ) ⊂ C [ x 0 , … , x n ] {\displaystyleSemi-invariant of a quiver (1,431 words) [view diff] exact match in snippet view article find links to article
quiver. ii) For each dimension vector d, the algebra SI(Q,d) is complete intersection. iii) For each dimension vector d, the algebra SI(Q,d) is eitherHodge structure (4,881 words) [view diff] exact match in snippet view article find links to article
2}={\frac {(d-1)(d-2)}{2}}} as desired. The Hodge numbers for a complete intersection are also readily computable: there is a combinatorial formula foundAbelian 2-group (1,503 words) [view diff] exact match in snippet view article find links to article
generalization. pg 88 One example is the cotangent complex for a local complete intersection scheme X {\displaystyle X} which is given by the two-term complexBase change theorems (4,151 words) [view diff] exact match in snippet view article find links to article
MR 0282985, OCLC 138290 Toën, Bertrand (2012), Proper local complete intersection morphisms preserve perfect complexes, arXiv:1210.2827, Bibcode:2012arXiv1210Residual intersection (3,349 words) [view diff] exact match in snippet view article find links to article
is possible to generalize the above construction and formula to complete intersection morphisms; this extension is discussed in § 6.6. as well as Ch.Virtual fundamental class (1,533 words) [view diff] exact match in snippet view article find links to article
situation should be emulated for a simple case (such as a smooth complete intersection). Suppose we have a variety X {\displaystyle X} (representing theSegre class (2,288 words) [view diff] exact match in snippet view article find links to article
given by π {\displaystyle \pi } . Let Z be a smooth curve that is a complete intersection of effective Cartier divisors D 1 , … , D n {\displaystyle D_{1}Erdős–Ko–Rado theorem (5,592 words) [view diff] exact match in snippet view article find links to article
Grindstaff (2020). Ahlswede, Rudolf; Khachatrian, Levon H. (1997), "The complete intersection theorem for systems of finite sets", European Journal of CombinatoricsNormal cone (3,349 words) [view diff] exact match in snippet view article find links to article
} Example: One has that X {\displaystyle X} is a local complete intersection if and only if C X = N X {\displaystyle {\mathfrak {C}}_{X}={\mathfrakAhlswede–Khachatrian theorem (2,051 words) [view diff] exact match in snippet view article find links to article
1996.0092. Ahlswede, Rudolf; Khachatrian, Levon H. (1997). "The complete intersection theorem for systems of finite sets". European Journal of CombinatoricsGlossary of commutative algebra (9,772 words) [view diff] exact match in snippet view article find links to article
ring that is a coherent module over itself. complete 1. A local complete intersection ring is a Noetherian local ring whose completion is the quotientSteven Sperber (1,781 words) [view diff] exact match in snippet view article find links to article
Alan; Sperber, Steven (2008). "On the zeta function of a projective complete intersection". Illinois Journal of Mathematics. 52 (2). doi:10.1215/ijm/1248355341