In mathematics, given an action of a group scheme G on a scheme X over a base scheme S, an equivariant sheafF on X is a sheaf of -modules together with the isomorphism of -modules
that satisfies the cocycle condition:[1][2] writing m for multiplication,
a group scheme G on a scheme X over a base scheme S, an equivariantsheaf F on X is a sheaf of O X {\displaystyle {\mathcal {O}}_{X}} -modules together...
F(X)G consists of equivariant sheaves on X; thus, the descent in this case says that to give an equivariantsheaf on X is to give a sheaf on the quotient...
individual D-modules (and not more general complexes thereof); a perverse sheaf is in general represented by a complex of sheaves. The concept of perverse...
_{3}}{\overset {\rho _{H_{2}\circ H_{1}}}{\to }}F_{\xi _{1}}} . (cf. equivariantsheaf.) The Hodge bundle on the moduli stack of algebraic curves of fixed...
over a field and the last nonzero term is the tangent sheaf, is called the Euler sequence. equivariant intersection theory See Chapter II of http://www.math...
level corresponds to that F {\displaystyle {\mathcal {F}}} is an equivariantsheaf with respect to an action of an affine group scheme G. It is a theorem...
frame bundle is useful because tensor fields on M can be regarded as equivariant vector-valued functions on F(M). On a manifold that is sufficiently smooth...
{\displaystyle H} is a closed 3-form. This construction was extended to equivariant K-theory and to holomorphic K-theory by Mathai and Stevenson. Bundle...
e)\cdot g=(x,e\cdot g)} It then follows that the map h covering f is equivariant and so defines a morphism of principal bundles. In the language of category...
In algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety...
conjecture on the Lefschetz trace formula (now called Fujiwara's theorem for equivariant correspondences). Brumer–Stark conjecture E7½ Hodge–de Rham spectral...
of equivariant cohomology. For example, Borel's theorem states that the cohomology ring of a classifying stack is a polynomial ring. l-adic sheaf smooth...
category of chiral algebras on X = A 1 {\displaystyle X=\mathbb {A} ^{1}} equivariant with respect to the group T {\displaystyle T} of translations. Chiral...
between cohomology with coefficients in a fixed abelian group A, and general sheaf cohomology in which coefficients vary from point to point. Local coefficient...
bundles), Wilfried Schmid (discrete series representations), Graeme Segal (equivariant K-theory), Alexander Shapiro (Clifford algebras), L. Smith (homotopy...
(such as a principal bundle), bundle morphisms are also required to be G-equivariant on the fibers. This means that φ : E → F {\displaystyle \varphi :E\to...
of topological modular forms is constructed as the global sections of a sheaf of E-infinity ring spectra on the moduli stack of (generalized) elliptic...
starting from, say, primitive spectra, it was not easy to develop a workable sheaf theory. One might imagine this difficulty is because of a sort of quantum...
the notion of smoothness from calculus. Instead it is built using sheaf theory and sheaf cohomology. Abstract harmonic analysis A modern branch of harmonic...
Society. p. ix. ISBN 9780821843284. Manolescu, Ciprian (2016), "Pin(2)-equivariant Seiberg–Witten Floer homology and the Triangulation Conjecture", Journal...
geometry. Motivated by the solution to the Cousin problems, he worked on sheaf cohomology and coherent sheaves and proved two powerful results, Cartan's...
sequence. The collection of all G-modules is a category (the morphisms are equivariant group homomorphisms, that is group homomorphisms f with the property...
locally constant sheaf A locally constant sheaf on a space X is a sheaf such that each point of X has an open neighborhood on which the sheaf is constant....
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