# THE GENERIC FIBRE OF MODULI SPACES OF BOUNDED LOCAL G-SHTUKAS

@article{Hartl2021THEGF, title={THE GENERIC FIBRE OF MODULI SPACES OF BOUNDED LOCAL G-SHTUKAS}, author={Urs Hartl and Eva Viehmann}, journal={Journal of the Institute of Mathematics of Jussieu}, year={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 generalise some very prominent concepts in the theory of Rapoport-Zink spaces to our setting. More precisely, we define period spaces, as well as the period map from a moduli space of bounded local G-shtukas to the corresponding period space, and we determine the image of the period map. Furthermore, we…

## 6 Citations

### The Carlitz Logarithm as a Period Morphism for Local $G$-Shtukas

- Mathematics
- 2019

Local shtukas are the function field analogs for $p$-divisible groups. Similar to the $p$-adic theory, one defines Rapoport-Zink functors and Rapoport-Zink spaces for these local shtukas. The…

### Uniformizing the Moduli Stacks of Global G-Shtukas

- MathematicsInternational Mathematics Research Notices
- 2019

This is the 2nd in a sequence of articles, in which we explore moduli stacks of global $\mathfrak{G}$-shtukas, the function field analogs for Shimura varieties. Here $\mathfrak{G}$ is a flat affine…

### 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…

### Extending torsors on the punctured Spec(A_inf)

- Mathematics
- 2018

For a parahoric group scheme over the ring of integers of a padic field we study the question whether a torsor defined on the punctured spectrum of Fontaine’s ring Ainf extends to the whole spectrum.…

### Extending torsors on the punctured Spec(Ainf)

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2022

Abstract We prove that torsors under parahoric group schemes on the punctured spectrum of Fontaine’s ring Ainf{A_{\mathrm{inf}}}, extend to the whole spectrum. Using descent we can extend a similar…

## References

SHOWING 1-10 OF 129 REFERENCES

### 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…

### The Newton stratification on deformations of local G-shtukas

- Mathematics
- 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…

### 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…

### Adequate moduli spaces and geometrically reductive group schemes

- Mathematics
- 2010

We introduce the notion of an adequate moduli space. The theory of adequate moduli spaces provides a framework for studying algebraic spaces which geometrically approximate algebraic stacks with…

### L-FUNCTIONS OF φ-SHEAVES AND DRINFELD MODULES

- Mathematics
- 1996

In this paper, we apply Dwork’s p-adic methods to study the meromorphic continuation and rationality of various L-functions arising from π-adic Galois representations, Drinfeld modules and φ-sheaves.…

### The Carlitz Logarithm as a Period Morphism for Local $G$-Shtukas

- Mathematics
- 2019

Local shtukas are the function field analogs for $p$-divisible groups. Similar to the $p$-adic theory, one defines Rapoport-Zink functors and Rapoport-Zink spaces for these local shtukas. The…

### The universal family of semistable p-adic Galois representations

- Mathematics
- 2020

Let $K$ be a finite field extension of $Q_p$ and let $G_K$ be its absolute Galois group. We construct the universal family of filtered $(\phi,N)$-modules, or (more generally) the universal family of…

### Uniformizing the Moduli Stacks of Global G-Shtukas

- MathematicsInternational Mathematics Research Notices
- 2019

This is the 2nd in a sequence of articles, in which we explore moduli stacks of global $\mathfrak{G}$-shtukas, the function field analogs for Shimura varieties. Here $\mathfrak{G}$ is a flat affine…

### Period Spaces for p-divisible Groups

- Mathematics
- 1995

In this monograph "p"-adic period domains are associated to arbitrary reductive groups. Using the concept of rigid-analytic period maps the relation of "p"-adic period domains to moduli space of…