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Foliations in deformation spaces of local G-shtukas
- Source :
-
Advances in Mathematics . Jan2012, Vol. 229 Issue 1, p54-78. 25p. - Publication Year :
- 2012
-
Abstract
- 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 surjective morphism on the closed Newton stratum of the universal deformation of a local G-shtuka, similarly to Oortʼs 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 229
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 67134329
- Full Text :
- https://doi.org/10.1016/j.aim.2011.08.011