The Newton stratification on deformations of local G-shtukas

Urs Hartl 1  and Eva Viehmann 2
  • 1 Mathematisches Institut, Universität Münster, Einsteinstr. 1, 48149 Münster, Germany
  • 2 Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

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 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 deformation 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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The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle’s Journal. In the 190 years of its existence, Crelle’s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals.

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