Foliations in deformation spaces of local G-shtukas

Details Foliations in deformation spaces of local G-shtukas Foliations in deformation spaces of local G-shtukas

2010-02-11

arxiv.org/abs/1002.2387v2

Mathematics

Algebraic Geometry

26 pages

Scientific paper

We study local G-shtukas with level structure over a base scheme whose Newton polygons are constant on the base. We show that after a finite base change and after passing to an \'etale covering, such a local G-shtuka is isogenous to a completely slope divisible one, generalizing corresponding results for p-divisible groups by Oort and Zink. As an application we establish a product structure up to finite morphism on the closed Newton stratum of the universal deformation of a local G-shtuka, similarly to Oort's foliations for p-divisible groups and abelian varieties. This also yields bounds on the dimensions of affine Deligne-Lusztig varieties and proves equidimensionality of affine Deligne-Lusztig varieties in the affine Grassmannian.

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