相关论文: A toy model for the Drinfeld-Lafforgue shtuka cons…
In this article we develop the theory of local models for the moduli stacks of global $G$-shtukas, the function field analogs for Shimura varieties. Here $G$ is a smooth affine group scheme over a smooth projective curve. As the first…
If a Quillen model category can be specified using a certain logical syntax (intuitively, ``is algebraic/combinatorial enough''), so that it can be defined in any category of sheaves, then the satisfaction of Quillen's axioms over any site…
We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke…
For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function $k\geq 0$ let $\mathbf N=N+\sum_{\alpha \in R} k(\alpha)$. We denote by $dw(\mathbf{x})=\Pi_{\alpha \in R}|\langle \mathbf{x},\alpha…
We construct the Fukaya category of a surface with genus greater than one and compute its Grothendieck group. We consider here a topological variant, in which we disregard the area form and use instead an admissibility condition borrowed…
The purpose of these lectures is to introduce the notion of a Stokes-perverse sheaf as a receptacle for the Riemann-Hilbert correspondence for holonomic D-modules. They develop the original idea of P. Deligne in dimension one, and make it…
A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on the intersection of two even dimensional quadrics is…
For every oriented surface of finite type, we construct a functorial Khovanov homology for links in a thickening of the surface, which takes values in a categorification of the corresponding gl(2) skein module. The latter is a mild…
We develop the theory of ind-geometric stacks, in particular their coherent and ind-coherent sheaf theory. This provides a convenient framework for working with equivariant sheaves on ind-schemes, especially in derived settings. Motivating…
We give a combinatorial description of the dg category of character sheaves on a complex reductive group $G$, extending results of [Li] for $G$ simply-connected. We also explicitly identify the parabolic induction/restriction functors.
We prove that the adjoint equivariant derived category of a reductive group $G$ is equivalent to the appropriately defined monoidal center of the torus-equivariant version of the Hecke category. We use this to give new proofs, independent…
Locality is implemented in an arbitrary category using Grothendieck topologies. We explore how different Grothendieck topologies on one category can be related, and, more general, how functors between categories can preserve them. As…
The purpose of this paper is to give a simpler proof to the problem of controllability of a Hilbert snake \cite{PeSa}. Using the action of the M\"obius group of the unit sphere on the configuration space, in the context of a separable…
Let l be a commutative ring with unit. Garkusha constructed a functor from the category of l-algebras into a triangulated category D, that is a universal excisive and homotopy invariant homology theory. Later on, he provided different…
Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on…
We derive a geometric model for the module category $\operatorname{mod} \mathbf{k} Q$ of a Dynkin quiver $Q$ via the heart of a total stability condition on the bounded derived category of $\operatorname{mod} \mathbf{k} Q$. As an…
We develop explicit formulas for Hecke operators of higher genus in terms of spherical coordinates. Applications are given to summation of various generating series with coefficients in local Hecke algebra and in a tensor product of such…
We construct functorial Igusa stacks for all Hodge-type Shimura varieties, proving a conjecture of Scholze and extending earlier results of the fourth-named author for PEL-type Shimura varieties. Using the Igusa stack, we construct a sheaf…
In this note we intend to look at the moduli stacks for global $G$-shtukas from a new perspective. We discuss a unifying interpretation of several moduli spaces (stacks) including moduli of global $G$-shtukas and (a variant of the) moduli…
This work investigates the Frobenius morphism on derived categories associated with algebraic stacks in positive characteristic. Particularly, we show that in many cases sufficiently many Frobenius pushforwards of a compact generator…