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Longer titles found: Locally constant sheaf (view)

searching for Constant sheaf 23 found (44 total)

Verdier duality (1,503 words) [view diff] exact match in snippet view article find links to article

n-dimensional manifold, k is a field and k X {\displaystyle k_{X}} is the constant sheaf on X with coefficients in k. Let f = p {\displaystyle f=p} be the constant

Beilinson–Bernstein localization (687 words) [view diff] exact match in snippet view article find links to article

along the T-bundle G/U → G/B, a sheaf of rings whose center is the constant sheaf of algebras U(t), and taking the quotient by the central character determined

De Rham theorem (1,493 words) [view diff] exact match in snippet view article find links to article

implies that the de Rham cohomology is the sheaf cohomology with the constant sheaf R {\displaystyle \mathbb {R} } . Thus, for abstract reason, the de Rham

Flat vector bundle (417 words) [view diff] exact match in snippet view article find links to article

differential forms Local system, the more general notion of a locally constant sheaf. Orientation character, a characteristic form related to the orientation

Leray spectral sequence (2,448 words) [view diff] exact match in snippet view article find links to article

generalized by instead considering sheaves of modules over a locally constant sheaf of rings A _ {\displaystyle {\underline {A}}} for a fixed commutative

Group scheme (2,860 words) [view diff] exact match in snippet view article find links to article

these are affine of infinite type. More generally, by taking a locally constant sheaf of groups on S, one obtains a locally constant group scheme, for which

Exceptional inverse image functor (707 words) [view diff] exact match in snippet view article find links to article

that below the last Q ℓ {\displaystyle \mathbb {Q} _{\ell }} means the constant sheaf on X {\displaystyle X} and the rest mean that on ∗ {\displaystyle *}

Complex analytic variety (1,306 words) [view diff] exact match in snippet view article find links to article

vanishing locus of a finite set of holomorphic functions. Denote the constant sheaf on a topological space with value C {\displaystyle \mathbb {C} } by

Injective sheaf (1,059 words) [view diff] exact match in snippet view article find links to article

consider a real manifold X. There is the following resolution of the constant sheaf R {\displaystyle \mathbb {R} } by the fine sheaves of (smooth) differential

Cousin problems (1,212 words) [view diff] exact match in snippet view article find links to article

{\exp }}\mathbf {O} ^{*}\to 0} where the leftmost sheaf is the locally constant sheaf with fiber 2 π i Z {\displaystyle 2\pi i\mathbb {Z} } . The obstruction

Cohomology with compact support (911 words) [view diff] exact match in snippet view article find links to article

R^{i}p_{!}{\mathcal {F}}.} Taking for F {\displaystyle {\mathcal {F}}} the constant sheaf with coefficients in a ring R {\displaystyle R} recovers the previous

Alexander duality (1,432 words) [view diff] exact match in snippet view article find links to article

if F = k _ {\displaystyle {\mathcal {F}}={\underline {k}}} is the constant sheaf and Y {\displaystyle Y} is a smooth submanifold, then we get Ext k n

Grothendieck trace formula (640 words) [view diff] exact match in snippet view article find links to article

{tr} (F_{E}\,\,|\,\,H_{c}^{i}(X_{\bar {k}},{\mathcal {F}}))} For a constant sheaf Q l {\displaystyle \mathbb {Q} _{l}} (viewed as ( lim ← ⁡ Z / l n Z

Motivic cohomology (2,552 words) [view diff] exact match in snippet view article find links to article

cohomology groups.) For example, Z(j) is zero for j < 0, Z(0) is the constant sheaf Z, and Z(1) is isomorphic in the derived category of X to Gm[−1]. Here

Weil conjectures (7,928 words) [view diff] exact match in snippet view article find links to article

_{i}\det(1-F^{*}t\mid H_{c}^{i}(F))^{(-1)^{i+1}}} The special case of the constant sheaf gives the usual zeta function. Verdier (1974), Serre (1975), Katz (1976)

Perverse sheaf (2,253 words) [view diff] exact match in snippet view article find links to article

regular) scheme over a henselian discrete valuation ring, then the constant sheaf shifted by dim ⁡ X + 1 {\displaystyle \dim X+1} is an étale perverse

Étale cohomology (5,016 words) [view diff] exact match in snippet view article find links to article

the usual singular cohomology of topological spaces, but in fact, any constant sheaf on an irreducible variety has trivial cohomology (all higher cohomology

Hodge structure (4,881 words) [view diff] exact match in snippet view article find links to article

structure of weight n on a complex manifold X consists of a locally constant sheaf S of finitely generated abelian groups on X, together with a decreasing

Differential form (10,077 words) [view diff] exact match in snippet view article find links to article

constant functions on M. Therefore, the complex is a resolution of the constant sheaf R, which in turn implies a form of de Rham's theorem: de Rham cohomology

Groupoid (6,206 words) [view diff] exact match in snippet view article find links to article

[\sigma ]\in {\check {H}}^{k}({\mathcal {U}},{\underline {A}})} for some constant sheaf of abelian groups can be represented as a function σ : ∐ U i 1 ⋯ i k

Algebraic torus (3,967 words) [view diff] exact match in snippet view article find links to article

H^{1}(S,GL_{n}(\mathbb {Z} ))} , where the coefficient group forms a constant sheaf. In particular, twisted forms of a split torus T over a field K are

Function of several complex variables (17,684 words) [view diff] exact match in snippet view article find links to article

{\exp } \mathbf {O} ^{*}\to 0} where the leftmost sheaf is the locally constant sheaf with fiber 2 π i Z {\displaystyle 2\pi i\mathbb {Z} } . The obstruction

T-structure (6,305 words) [view diff] exact match in snippet view article find links to article

a smooth open subscheme and F U {\displaystyle F_{U}} is a locally constant sheaf on U. Note the presence of the shift according to the dimension of Z