Related papers: Local systems with restricted variation on the for…

We define a new geometric object--the stack of local systems with restricted variation. We formulate a version of the categorical geometric Langlands conjecture that makes sense for any constructible sheaf theory (such as l-adic sheaves).…

We introduce a family of rank-one local systems in the category of twisted $\mathcal{D}$-modules on a certain subvariety isomorphic to ${\mathbb{G}_{\text{m}}}^2$ of the affine flag variety of $\text{SL}_2$. We then give a criterion for…

In this paper we study the local geometry of the stack of pointed $A_r$-stable curves. In particular, we analyze the deformation theory of $A_r$-stable curves and their automorphism groups in order to study the combinatorics of families of…

In this work we discuss a new type of factorisation systems for \textbf{Ord}-enriched categories. We start by defining the new notion of lax weak orthogonality, which involves the existence of lax diagonal morphisms for lax squares. Using…

Given a category fibered in groupoids over schemes with a log structure, one produces a category fibered in groupoids over log schemes. We classify the groupoid fibrations over log schemes that arise in this manner in terms of a categorical…

Much recent work has been done on the local Fourier transforms for connections on the punctured formal disk. Specifically, the local Fourier transforms have been introduced, shown to induce certain equivalences of categories, and explicit…

We construct the moduli stack of torsors over the formal punctured disk in characteristic p > 0 for a finite group isomorphic to the semidirect product of a p-group and a tame cyclic group. We prove that the stack is a limit of separated…

In "On the calculation of some differential Galois groups" (Invent. Math. 87 (1987), no. 1), Katz defines the notion of a special flat connection on the complex affine line minus the origin, and he shows that the functor which restricts a…

We extend the notion of a factorization system in a category to the realm of $\infty$-categories. To this end, we provide a description of the category of $\infty$-categories with factorization systems as the category of presheaves of…

We study algebraic (Artin) stacks over $\bar{\mathcal M}_g$ giving a functorial way of compactifying the relative degree $d$ Picard variety for families of stable curves. We also describe for every $d$ the locus of genus $g$ stable curves…

We introduce the concept of multiplicatively closed subsets of a commutative ring $R$ which split an $R$-module $M$ and study factorization properties of elements of $M$ with respect to such a set. Also we demonstrate how one can utilize…

We study moduli spaces of truncated local shtukas and truncated displays and describe them as concrete quotient stacks. To do this, we develop a general formalism of frames that can be applied in both cases and is also used to study…

We study locally presentable categories equipped with a cofibrantly generated weak factorization system. Our main result is that these categories are closed under 2-limits, in particular under pseudopullbacks. We give applications to…

We calculate the local Fourier transforms for connections on the formal punctured disk, corroborating the results of J. Fang and C. Sabbah using a different method. Our method is similar to Fang's, but more direct.

This paper is a continuation of an earlier paper of the authors on the probem of specializations of modules. The aim here is to define specialisations of finitely generated modules over local rings of the form k(u)[X]_P, where u is a family…

We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…

We study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes. This is possible surprisingly often: we show that many of the standard examples of moduli stacks are determined by their…

The local structure of a tiling is described in terms of a multiplicative structure on its pattern classes. The groupoid associated to the tiling is derived from this structure and its integer group of coinvariants is defined. This group…

We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently…

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…