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

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.

58 pages, significant improvements and corrections compared to the first version; to appear in Journal Inst. Math. Jussieu

References in corpus (5)

• Revêtements étales et groupe fondamental (SGA 1)
• Rapoport-Zink spaces for spinor groups
• On parahoric subgroups
• Local P-shtukas and their relation to global G-shtukas
• Foliations and the cohomology of moduli spaces of bounded global $G$-shtukas

Cited by in corpus (3)

• Extending torsors on the punctured Spec(A_inf)
• Rapoport-Zink Spaces For Local P-Shtukas and Their Local Models
• The Carlitz Logarithm as a Period Morphism for Local $G$-Shtukas