Related papers: Local Models For The Moduli Stacks of Global $G$-S…
This is the second in a sequence of articles, in which we explore moduli stacks of global G-shtukas, the function field analogs for Shimura varieties. Here G is a flat affine group scheme of finite type over a smooth projective curve C over…
This is the first in a sequence of two articles investigating moduli stacks of global G-shtukas, which are function field analogs for Shimura varieties. Here G is a flat affine group scheme of finite type over a smooth projective curve, and…
In this article we first survey the analogy between Shimura varieties (resp. Rapoport-Zink spaces) and moduli stacks for global G-shtukas (resp. Rapooprt Zink spaces for local P-shtukas). This part is intended to enrich the dictionary…
This article provides a ``local'' complementary to the previous results concerning the local models for the moduli stacks of ``global'' $G$-shtukas. Here we study the geometry of Rapoport-Zink spaces for local $P$-shtukas by constructing…
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…
For arbitrary reductive groups $G$ defined over a finite field, we decompose Newton strata in the special fiber of moduli spaces of global $G$-shtukas into a product of Rapoport-Zink spaces and Igusa varieties. This allows us to compare the…
Moduli spaces of bounded local $G$-shtukas are a group-theoretic generalization of the function field analog of Rapoport and Zink's moduli spaces of $p$-divisible groups. In this article we generalize some very prominent concepts in the…
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…
Two approaches to the construction of integral models of local Shimura-varieties are compared: that of B\"ultel-Pappas using $\mathcal{G}$-$\mu$-displays and that of Scholze using local mixed-characteristic shtuka. As an application, the…
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…
Bounded local G-shtukas are function field analogs for p-divisible groups with extra structure. We describe their deformations and moduli spaces. The latter are analogous to Rapoport-Zink spaces for p-divisible groups. The underlying…
In this paper we classify isogeny classes of global $\mathsf{G}$-shtukas over a smooth projective curve $C/\mathbb{F}_q$ (or equivalently $\sigma$-conjugacy classes in $\mathsf{G}(\mathsf{F} \otimes_{\mathbb{F}_q} \overline{\mathbb{F}_q})$…
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…
In this article we formulate and prove the analogue of the Langlands-Rapoport conjecture for the moduli stacks of global $G$-shtukas. Here $G$ is a parahoric Bruhat-Tits group scheme over a smooth projective curve $C$ over a finite field…
Local models are schemes defined in linear algebra terms that describe the 'etale local structure of integral models for Shimura varieties and other moduli spaces. We point out that the flatness conjecture of Rapoport-Zink on local models…
We give an overview of the theory of local G-shtukas and their moduli spaces that were introduced in joint work of U.~Hartl and the author, and in the past years studied by many people. We also discuss relations to moduli of global…
We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, as well as their resolutions by moduli stacks of two-dimensional Breuil-Kisin modules with tame descent data. We study…
We study topological properties of moduli spaces of p-adic shtukas and local Shimura varieties. On one hand, we construct and study the specialization map for moduli spaces of p-adic shtukas at parahoric level whose target is an affine…
Let \(G\) be a reductive group over a field \(k\), and let \(\mu\) be a cocharacter of \(G\). We prove that Viehmann's double coset spaces associated with \((G, \mu)\) are representable by certain Lusztig varieties, and establish a similar…
We give a construction of "integral local Shimura varieties" which are formal schemes that generalize the well-known integral models of the Drinfeld $p$-adic upper half spaces. The construction applies to all classical groups, at least for…