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The Newton stratification on deformations of local G-shtukas

Urs Hartl, Eva Viehmann (Univ. Bonn)
published 2011-04-19

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 deforma- tion of a local G-shtuka is isomorphic to the completion of a corresponding affine Deligne-Lusztig variety in that point. This yields bounds on the dimension and proves equidimensionality of the basic affine Deligne-Lusztig varieties.

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