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1.
The space spanned by the class of simple perverse sheaves in Zheng (2008) without localization is isomorphic to the tensor product of a Verma module with a tensor product of irreducible integrable highest weight modules of the quantum enveloping algebra associated with a graph. Under the isomorphism, the simple perverse sheaves get identified with the canonical basis elements of the tensor product module. The two stability conditions coincide with the localization process in Zheng (2008), by using supports and singular supports of complexes of sheaves, respectively.  相似文献   

2.
We give a generic estimation of trigonometric sums defined over closed sub-schemes with semi-stable reduction of the standard affine scheme modulo pn(n 2). We use Greenberg realisation to reduce to trigonometric sums defined over smooths sub-schemes of a finite product of Witt vectors over the finite field of p elements. Using the cohomological interpretation of this sums over a finite field, the sum is directly related to the Fourier–Deligne transformation of the dual pairs of Witt vectors. We deduce the estimation from the properties of the Fourier–Deligne transformation on simple perverse sheaves and pure sheaves.  相似文献   

3.
We give sufficient conditions on Banach spaces X and Y so that their projective tensor product Xπ Y, their injective tensor product Xɛ Y, or the dual (Xπ Y)* contain complemented copies of ℓp.  相似文献   

4.
5.
We give a construction of torsionfree sheaves on a seminormal variety Y using torsionfree sheaves on the normalization X and the non-normal locus W. We use it to find a relation between Picard groups of X, Y, and W. We apply it to determine the Picard groups of the generalized Jacobian, the compactified Jacobian and some subschemes associated to the moduli spaces of torsionfree sheaves of rank 2 and odd degree on a nodal curve.  相似文献   

6.
Given two smooth projective varieties X and Y, X is defined to motivate Y if the motive of Y is contained in the tensor category generated by X. Some techniques are given for checking this condition. It is shown that in a number of cases moduli spaces of sheaves over curves or surfaces are motivated by the underlying curve or surface. This is used to check the Hodge and related conjectures for some of these examples.  相似文献   

7.
Contrary to a recent conjecture, it is shown that weakly compact subsets of the projective tensor product of Banach spaces X and Y in general are not contained in the closed absolutely convex hull of a tensor product AB of weakly compact subsets A of X and B of Y.  相似文献   

8.
The aim of this work is to give a generalization of Gabriel’s Theorem on coherent sheaves to coherent twisted sheaves on noetherian schemes. We start by showing that we can recover a noetherian scheme X from the category Coh(X, α) of coherent α-twisted sheaves over X, where α lies in the cohomological Brauer group of X. This follows from the bijective correspondence between closed subsets of X and Serre subcategories of finite type of Coh(X, α). Moreover, any equivalence between Coh(X, α) and Coh(Y, β), where X and Y are noetherian schemes, and , β Br ′(Y) induces an isomorphism between X and Y.  相似文献   

9.
In this paper we study equivalent formulations of the DP? Pp (1 < p < ∞). We show that X has the DP? Pp if and only if every weakly-p-Cauchy sequence in X is a limited subset of X. We give su?cient conditions on Banach spaces X and Y so that the projective tensor product X ?π Y, the dual (X ?? Y)? of their injective tensor product, and the bidual (X ?π Y)?? of their projective tensor product, do not have the DP Pp, 1 < p < ∞. We also show that in some cases, the projective and the injective tensor products of two spaces do not have the DP? Pp, 1 < p < ∞.  相似文献   

10.
We extend the notion of a parabolic vector bundle on a smooth curve to define generalized parabolic sheaves (GPS) on any integral projective curve X. We construct the moduli spacesM(X) of GPS of certain type onX. IfX is obtained by blowing up finitely many nodes inY then we show that there is a surjective birational morphism from M(X) to M (Y). In particular, we get partial desingularisations of the moduli of torsion-free sheaves on a nodal curveY.  相似文献   

11.
Let X be a scheme of finite type over a Noetherian base scheme S admitting a dualizing complex, and let UX be an open set whose complement has codimension at least 2. We extend the Deligne-Bezrukavnikov theory of perverse coherent sheaves by showing that a coherent intermediate extension (or intersection cohomology) functor from perverse sheaves on U to perverse sheaves on X may be defined for a much broader class of perversities than has previously been known. We also introduce a derived category version of the coherent intermediate extension functor.Under suitable hypotheses, we introduce a construction (called “S2-extension”) in terms of perverse coherent sheaves of algebras on X that takes a finite morphism to U and extends it in a canonical way to a finite morphism to X. In particular, this construction gives a canonical “S2-ification” of appropriate X. The construction also has applications to the “Macaulayfication” problem, and it is particularly well-behaved when X is Gorenstein.Our main goal, however, is to address a conjecture of Lusztig on the geometry of special pieces (certain subvarieties of the unipotent variety of a reductive algebraic group). The conjecture asserts in part that each special piece is the quotient of some variety (previously unknown for the exceptional groups and in positive characteristic) by the action of a certain finite group. We use S2-extension to give a uniform construction of the desired variety.  相似文献   

12.
Achar has recently introduced a family of t-structures on the derived category of equivariant coherent sheaves on a G-scheme, generalizing the perverse coherent t-structures of Bezrukavnikov and Deligne. They are called staggered t-structures, and one of their points of interest is that they are more often self-dual. In this paper we investigate these t-structures on the T-equivariant derived category of a toric variety.  相似文献   

13.
In this paper we prove that the Fremlin tensor product of two f-algebras can be endowed with an f-algebra structure and satisfies an appropriate universal property. In particular, the Riesz tensor product of C(X) and C(Y), where X and Y are topological spaces, is an f-subalgebra of C(X × Y).  相似文献   

14.
We study the category 𝒞(X, Y) generated by an exceptional pair (X, Y) in a hereditary category ?. If r = dim k Hom(X, Y) ≥ 1 we show that there are exactly 3 possible types for 𝒞(X, Y), all derived equivalent to the category of finite dimensional modules mod(H r ) over the r-Kronecker algebra H r . In general 𝒞(X, Y) will not be equivalent to a module category. More specifically, if ? is the category of coherent sheaves over a weighted projective line 𝕏, then 𝒞(X, Y) is equivalent to the category of coherent sheaves on the projective line ?1 or to mod(H r ) and, if 𝕏 is wild, then every r ≥ 1 can occur in this way.  相似文献   

15.
Let X be a smooth toric variety stratified by the torus action. From the fan associated to X we define a category of quiver representations equivalent to the category of perverse sheaves on X relatively to the fixed stratification.  相似文献   

16.
Let X be a Banach space with the Grothendieck property, Y a reflexive Banach space, and let X ⊗̌ɛ Y be the injective tensor product of X and Y.
(a)  If either X** or Y has the approximation property and each continuous linear operator from X* to Y is compact, then X ⊗̌ɛ Y has the Grothendieck property.  相似文献   

17.
We study the tensor product of two directed Archimedean partially ordered vector spaces X and Y by means of Riesz completions. With the aid of the Fremlin tensor product of the Riesz completions of X and Y we show that the projective cone in X ? Y is contained in an Archimedean cone. The smallest Archimedean cone containing the projective cone satisfies an appropriate universal mapping property.  相似文献   

18.

This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.

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19.
It was proved by Ginzburg, Mirkovic and Vilonen that the G(O)-equivariant perverse sheaves on the affine Grassmannian of a connected reductive group G form a tensor category equivalent to the tensor category of finite dimensional representations of the dual group G . In this paper we construct explicitly the action of G on the global cohomology of a perverse sheaf.  相似文献   

20.
Bezrukavnikov, later together with Arinkin, recovered Deligne’s work defining perverse t-structures in the derived category of coherent sheaves on a projective scheme. We prove that these t-structures can be obtained through tilting with respect to torsion theories, as in the work of Happel, Reiten and Smalø. This approach allows us to define, in the quasi-coherent setting, similar perverse t-structures for certain noncommutative projective planes.  相似文献   

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