Related papers: On purity theorem of Lusztig's perverse sheaves

In this paper we prove a new generic vanishing theorem for $X$ a complete homogeneous variety with respect to an action of a connected algebraic group. Let $A, B_0\subset X$ be locally closed affine subvarieties, and assume that $B_0$ is…

Using Saito's theory of mixed Hodge modules, we study a generalization of Hellus-Schenzel's "cohomologically complete intersection" property. This property is equivalent to perversity of the shifted constant sheaf. We relate the generalized…

v2: For a projective variety defined over a finite field with $q$ elements, it is shown that as algebraic integers, the eigenvalues of the geometric Frobenius acting on $\ell$-adic cohomology have higher than known $q$-divisibility beyond…

We show that the Borel-equivariant derived category of sheaves on the flag variety of a complex reductive group is equivalent to the perfect derived category of dg modules over the extension algebra of the direct sum of the simple…

We define a quantum analogue of the Grothendieck ring of finite dimensional modules of a quantum affine algebra of simply laced type. The construction is based on perverse sheaves on a variety related to quivers. We get also a new geometric…

Let ($\mathfrak{g},\mathsf{g})$ be a pair of complex finite-dimensional simple Lie algebras whose Dynkin diagrams are related by (un)folding, with $\mathsf{g}$ being of simply-laced type. We construct a collection of ring isomorphisms…

We prove that in either the convergent or overconvergent setting, an absolutely irreducible $F$-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic $p$, further equipped with actions of the…

Let $g$ be a semi-simple simply-connected Lie algebra and let $U_\ell$ be the corresponding quantum group with divided powers, where $\ell$ is an even order root of unity. Let in addition $u_\ell\subset U_\ell$ be the corresponding "small"…

It is well known that "Fukaya category" is in fact an $A_{\infty}$-pre-category in sense of Kontsevich and Soibelman \cite{KS}. The reason is that in general the morphism spaces are defined only for transversal pairs of Lagrangians, and…

Let $X$ be a smooth projective variety of dimension $n$, and let $E$ be an ample vector bundle over $X$. We show that any non-zero Schur class of $E$, lying in the cohomology group of bidegree $(n-1, n-1)$, has a representative which is…

Kazhdan and Lusztig identified the affine Hecke algebra $\mathcal{H}$ with an equivariant $K$-group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of…

We show for an affine variety $X$, the derived category of quasi-coherent $D$-modules is equivalent to the category of DG modules over an explicit DG algebra, whose zeroth cohomology is the ring of Grothendieck differential operators…

It has been shown in this paper that the commutative Frobenius algebra $QZ_5\otimes Z(QS_3)$ provides a complete invariant for two-dimensional cobordisms, i.e., that the corresponding two-dimensional quantum field theory is faithful. The…

We determine the structure modulo p of the de Rham-Witt complex of a smooth scheme X over a discrete valuation ring of mixed characteristic with log-poles along the special fiber Y and show that the sub-sheaf fixed by the Frobenius is…

We give a complete quiver description of the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the…

We define and study a relative perverse $t$-structure associated with any finitely presented morphism of schemes $f: X\to S$, with relative perversity equivalent to perversity of the restrictions to all geometric fibres of $f$. The…

In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic. In particular, we show that if the…

We propose the notion of a supercategory as an alternative approach to supermathematics. We show that this setting is rich to carry out many of the basic constructions of supermathematics. We also prove generalizations of a number of…

For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivariant $E$-theory of the $C^*$-algebra of…

The coefficients of the Kazhdan-Lusztig polynomials $P_{v,w}(q)$ are nonnegative integers that are upper semicontinuous on Bruhat order. Conjecturally, the same properties hold for $h$-polynomials $H_{v,w}(q)$ of local rings of Schubert…