相关论文: A toy model of shtukas

We present a decomposition of the space of twisted arcs of a toric stack. As a consequence, we give a combinatorial description of the motivic integral associated to a torus-invariant divisor of a toric stack.

Moduli spaces of global $\mathbb G$-shtukas play a crucial role in the Langlands program for function fields. We analyze their functoriality properties following a change of the curve and a change of the group scheme $\mathbb G$ under…

We prove an analogue for Stokes torsors of Deligne's skeleton conjecture and deduce from it the representability of the functor of relative Stokes torsors by an affine scheme of finite type over C. This provides, in characteristic 0, a…

We make a detailed account of sign-normalized rank 1 Drinfeld A-modules, for A the coordinate ring of an elliptic curve over a finite field, in order to provide a parallel theory to the Carlitz module for F_q[t]. Using precise formulas for…

We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using Geometric Invariant Theory and the anticanonical…

We develop the analog of crystalline Dieudonn\'e theory for p-divisible groups in the arithmetic of function fields. In our theory p-divisible groups are replaced by divisible local Anderson modules, and Dieudonn\'e modules are replaced by…

We present some features of the smooth structure, and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance of these structures - it allows us to talk about the…

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…

Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the…

In this paper, we consider diffeological spaces as stacks over the site of smooth manifolds, as well as the "underlying" diffeological space of any stack. More precisely, we consider diffeological spaces as so-called concrete sheaves and…

In this paper, we propose a definition of the moduli stack of stable relative ideal sheaves, and prove that it is a separated and proper Deligne-Mumford stack. It is the first part of the project of relative Donaldson-Thomas theory of ideal…

We study $\mathscr{D}$-elliptic sheaves in terms of their associated modules, which we call Drinfeld-Stuhler modules. We prove some basic results about Drinfeld-Stuhler modules and their endomorphism rings, and then examine the existence…

We introduce the moduli stack of pointed curves equipped with effective $r$-spin structures: these are effective divisors $D$ such that $rD$ is a canonical divisor modified at marked points. We prove that this moduli space is smooth and…

We contribute to the foundations of tropical geometry with a view towards formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for the moduli space of curves and show…

For a split reductive group G over a finite field, we show that the intersection (cohomology) motive of the moduli stack of iterated G-shtukas with bounded modification and level structure is defined independently of the standard…

The moduli space of canonical divisors (with prescribed zeros and poles) on nonsingular curves is not compact since the curve may degenerate. We define a proper moduli space of twisted canonical divisors in the moduli space of…

We show that the module of Stark units associated to a sign-normalized rank one Drinfeld module can be obtained from Anderson's equivariant $A$-harmonic series. We apply this to obtain a class formula \`a la Taelman and to prove a several…

In this article we study motives corresponding to the moduli stacks of G-shtukas and their local models. In particular we deal with the question of describing their motivic fundamental invariants. As an application, we provide a criterion…

We show that the moduli spaces of bounded global $\mathcal{G}$-Shtukas with pairwise colliding legs admit $p$-adic uniformization isomorphisms by Rapoport-Zink spaces. Here $\mathcal{G}$ is a smooth affine group scheme with connected fibers…

In this paper we give construct good moduli spaces for constructible sheaves and Stokes functors. Derived enhancement of such are also considered.