The generic fiber of moduli spaces of bounded local $G$-shtukas

Urs Hartl; Eva Viehmann

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arXiv · 1712.07936

The generic fiber of moduli spaces of bounded local $G$-shtukas

Urs Hartl·Eva Viehmann

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Abstract

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 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 define a tower of coverings of the generic fiber of the moduli space which is equipped with a Hecke action and an action of a suitable automorphism group. Finally we consider the $\ell$-adic cohomology of these towers.

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BibTeX RIS

Urs Hartl, Eva Viehmann. 2017-12-21. The generic fiber of moduli spaces of bounded local $G$-shtukas. https://arxiv.org/abs/1712.07936

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