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Longer titles found: Locally constant sheaf (view)

searching for Constant sheaf 19 found (44 total)

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

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 (1,305 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 (2,437 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

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

Weil conjectures (7,942 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)

Differential form (10,058 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 (6,214 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

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

Function of several complex variables (17,688 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