Foliations in deformation spaces of local G-shtukas

Abstract

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 étale 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.

26 pages

References in corpus (6)

• The Newton stratification on deformations of local G-shtukas
• Résolutions de Demazure affines et formule de Casselman-Shalika géométrique
• Affine Deligne-Lusztig varieties in affine flag varieties
• A Dictionary between Fontaine-Theory and its Analogue in Equal Characteristic
• The global structure of moduli spaces of polarized p-divisible groups
• Truncations of level 1 of elements in the loop group of a reductive group

Cited by in corpus (9)

• Local P-shtukas and their relation to global G-shtukas
• Irreducible components of minuscule affine Deligne-Lusztig varieties
• The almost product structure of Newton strata in the Deformation space of a Barsotti-Tate group with crystalline Tate tensors
• Truncations of level 1 of elements in the loop group of a reductive group
• Foliations and the cohomology of moduli spaces of bounded global $G$-shtukas
• The generic fiber of moduli spaces of bounded local $G$-shtukas
• Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic
• On central leaves of Hodge-type Shimura varieties with parahoric level structure
• Newton strata in the loop group of a reductive group