Related papers: Tannaka duality and 1-affineness

We formulate and prove Chevalley's theorem in the setting of affine Nash groups. As a consequence, we show that the semi-direct product of two almost linear Nash groups is still an almost linear Nash group.

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

We show that we can release the rigidity of the skew Howe duality process for ${\mathfrak sl}_n$ knot invariants by rescaling the quantum Weyl group action, and recover skein modules for web-tangles. This skew Howe duality phenomenon can be…

The paper is devoted to modal properties of the ternary strict betweenness relation as used in the development of various systems of geometry. We show that such a relation is non-definable in a basic similarity type with a binary operator…

We develop the technique of weight truncation in the context of wall-crossings in birational cobordisms, parallel to that in [HL15, BFK19]. More precisely, for each such wall-crossing, we embed the bounded above derived category of coherent…

In this paper we prove a duality for constructible sheaves on conically smooth stratified spaces. Here we consider sheaves with values in a stable and bicomplete $\infty$-category equipped with a closed symmetric monoidal structure, and in…

Motivated by applications to the categorical and geometric local Langlands correspondences, we establish an equivalence between the category of filtered $\mathcal{D}$-modules on a smooth stack $X$ and the category of $S^1$-equivariant…

We define the tensor product of filtered $A_\infty$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical…

We calculate the category of D-modules on the loop space of the affine line in coherent terms. Specifically, we find that this category is derived equivalent to the category of ind-coherent sheaves on the moduli space of rank one de Rham…

We prove that the strange duality conjecture of Beauville-Donagi-Tu holds for all curves. We establish first a more extended rank-level duality, interesting in its own right, from which the standard rank-level duality follows by…

Let $\mathcal{G}$ be a finite 2-group. We show that the 2-category $2\mathrm{Rep}(\mathcal{G})$ of finite semisimple 2-representations is a symmetric fusion 2-category. We also relate the auto-equivalence 2-group of the symmetric monoidal…

We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations…

Generalizing the theory of parity sheaves on complex algebraic stacks due to Juteau-Mautner-Williamson, we develop a theory of twisted equivariant parity sheaves. We use this formalism to construct a modular incarnation of Lusztig and Yun's…

In this paper we translate the necessary and sufficient conditions of Tanaka's theorem on the finiteness of effective prolongations of a fundamental graded Lie algebras into computationally effective criteria, involving the rank of some…

We show that Bloch's complex of relative zero-cycles can be used as a dualizing complex over perfect fields and number rings. This leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over…

The proximinality of certain subspaces of spaces of bounded affine functions is proved. The results presented here are some linear versions of an old result due to Mazur. For the proofs we use some sandwich theorems of Fenchel's duality…

We study the \'etale sheafification of algebraic K-theory, called \'etale K-theory. Our main results show that \'etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories.…

We prove a K\"unneth-type equivalence of derived categories of lisse and constructible Weil sheaves on schemes in characteristic $p > 0$ for various coefficients, including finite discrete rings, algebraic field extensions $E \supset…

The theory of $\Theta$-stratifications generalizes a classical stratification of the moduli of vector bundles on a smooth curve, the Harder-Narasimhan-Shatz stratification, to any moduli problem that can be represented by an algebraic…

For an arbitrary $\infty$-topos, we classify the smashing localizations in the $\infty$-category of sheaves valued in derived vector spaces: Any of them is the restriction functor to a (unique) closed subtopos. Our proof is based on the…