# The Newton stratification on deformations of local G-shtukas

@inproceedings{Hartl2008TheNS, title={The Newton stratification on deformations of local G-shtukas}, author={Urs Hartl and Eva Viehmann}, year={2008} }

Abstract 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 schemes of these moduli spaces are affine Deligne–Lusztig varieties. For basic Newton polygons the closed Newton stratum in the universal deformation of a local G-shtuka is isomorphic to the completion of a corresponding affine Deligne–Lusztig variety in…

## 49 Citations

### Foliations and the cohomology of moduli spaces of bounded global G-shtukas

- Mathematics
- 2016

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 decomposition holds as well for associated adic…

### MODULI SPACES OF LOCAL G-SHTUKAS

- MathematicsProceedings of the International Congress of Mathematicians (ICM 2018)
- 2019

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…

### On the geometric connected components of moduli spaces of p-adic shtukas and local Shimura varieties

- Mathematics
- 2021

We study connected components of local Shimura varieties. Given local shtuka datum (G, b, μ), with G unramified over Qp and (b, μ) HN-irreducible, we determine π0(ShtG,b,[μ],∞×Cp) with its G(Qp)×…

### Local shtukas, Hodge–Pink structures and Galois representations

- Mathematics$t$-Motives: Hodge Structures, Transcendence and Other Motivic Aspects
- 2020

We review the analog of Fontaine's theory of crystalline p-adic Galois representations and their classification by weakly admissible filtered isocrystals in the arithmetic of function fields over a…

### Local P-shtukas and their relation to global G-shtukas

- Mathematics
- 2014

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…

### Functoriality of Moduli Spaces of Global $\mathbb G$-Shtukas

- Mathematics
- 2019

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 GENERIC FIBRE OF MODULI SPACES OF BOUNDED LOCAL G-SHTUKAS

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2021

Moduli spaces of bounded local G-shtukas are a group-theoretic generalisation of the function field analogue of Rapoport and Zink’s moduli spaces of p-divisible groups. In this article we…

### Affine Deligne–Lusztig varieties in affine flag varieties

- MathematicsCompositio Mathematica
- 2010

Abstract This paper studies affine Deligne–Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them…

### Local Models For Moduli Spaces For Local P-Shtukas

- Mathematics
- 2020

In this article we study local properties of Rapoport-Zink spaces for local $\mathbb{P}$-shtukas by constructing local models for them. This provides a "local" complementary to the previous results…

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