The Newton stratification on deformations of local G-shtukas

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.

several improvements, definition of local G-shtuka is changed

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Cited by in corpus (22)

• A Dictionary between Fontaine-Theory and its Analogue in Equal Characteristic
• Local P-shtukas and their relation to global G-shtukas
• Foliations in deformation spaces of local G-shtukas
• Local Shtukas and Divisible Local Anderson Modules
• Irreducible components of minuscule affine Deligne-Lusztig varieties
• The universal family of semi-stable p-adic Galois representations
• Local Shtukas, Hodge-Pink Structures and Galois Representations
• Local Models For The Moduli Stacks of Global $G$-Shtukas
• Foliations and the cohomology of moduli spaces of bounded global $G$-shtukas
• Langlands-Rapoport Conjecture Over Function Fields
• The generic fiber of moduli spaces of bounded local $G$-shtukas
• Rapoport-Zink Spaces For Local P-Shtukas and Their Local Models
• Category Of C-Motives Over Finite Fields
• Integral models of moduli spaces of shtukas with deep Bruhat-Tits level structures
• Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic
• Compactification of Level Maps of Moduli Spaces of Drinfeld Shtukas
• Dimensions of affine Deligne-Lusztig varieties in affine flag varieties
• The Carlitz Logarithm as a Period Morphism for Local $G$-Shtukas
• Newton strata in the loop group of a reductive group
• Geometric Structure of Affine Deligne-Lusztig Varieties for $G{L}_3$
• Point Counting on Igusa Varieties for function fields
• Deformations and elements of deformation theory