Related papers: A categorical K\"unneth formula for constructible …

Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this thesis we study constructions of cocomplete…

Let $k$ be a perfect field of characteristic $p$ and $W(k)$ its ring of Witt vectors. We construct an equivalence of categories between the full subcategory of the derived category of quasi-coherent sheaves on the syntomification of $W(k)$…

The classical construction of the Weil representation, with complex coefficients, has long been expected to work for more general coefficient rings. This paper exhibits the minimal ring $\mathcal{A}$ for which this is possible, the integral…

Let S be a Noetherian scheme and f:X -> S a proper morphism. By SGA 4 XIV, for any constructible sheaf F of Z/nZ-modules on X, the sheaves of Z/nZ-modules R^if_*F obtained by direct image (for the etale topology) are also constructible:…

The manuscript at hand systematically studies K\"unneth formulas at a categorical level. We give criteria for an abstract six functor formalism to satisfy the categorical K\"unneth formula, and use this to formulate conjectures for…

A wide class of skew derivations on degree-one generalized Weyl algebras $R(a,\varphi)$ over a ring $R$ is constructed. All these derivations are twisted by a degree-counting extensions of automorphisms of $R$. It is determined which of the…

We obtain a linear algebra data presentation of the category of constructible with respect to perverse triangulation sheaves on a finite simplicial complex. We also establish Koszul duality between the above mentioned category and the…

We introduce in this note the notion of the category of twisted Chow-Witt correspondences $CHW(k)$ over a field $k$ of characteristic different from $2$. Moreover, we show that over an infinite perfect field this category $CHW(k)$ admits a…

We study non-commutative projective lines over not necessarily algebraic bimodules. In particular, we give a complete description of their categories of coherent sheaves and show they are derived equivalent to certain bimodule species. This…

We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a…

We prove a formula for the structure sheaf of a quiver variety in the Grothendieck ring of its embedding variety. This formula generalizes and gives new expressions for Grothendieck polynomials. We furthermore conjecture that the…

A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations.…

Flach and Morin constructed in (Doc. Math. 23 (2018), 1425--1560) Weil-\'etale cohomology $H^i_\text{W,c} (X, \mathbb{Z} (n))$ for a proper, regular arithmetic scheme $X$ (i.e. separated and of finite type over $\operatorname{Spec}…

Let $G$ be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic $p$. Let $I$ be a pro-$p$ Iwahori subgroup of $G$ and let $R$ be a commutative quasi-Frobenius ring. If…

We are going to show that the sheafication of graded Koszul modules $% K_{\Gamma}$ over $\Gamma_{n}=K[ x_{0},x_{1}...x_{n}] $ form an important subcategory $\overset{\wedge}{K}_{\Gamma}$ of the coherents sheaves on projective space,…

We construct all finite irreducible modules over Lie conformal superalgebras of type K

This article contains a proof of the basic lemma. This lemma, discovered by Beilinson, yields a motivic proof of the Andreotti-Frankel theorem for affine varieties. Next, it is shown that the category of Cohomologically Constructible…

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical…

This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $K$-theory). These dualities are expressed in terms of…

We develop a "Soergel theory" for Bruhat-constructible perverse sheaves on the flag variety $G/B$ of a complex reductive group $G$, with coefficients in an arbitrary field $\Bbbk$. Namely, we describe the endomorphisms of the projective…