Affine Grassmannians and the geometric Satake in mixed characteristic

Abstract

We endow the set of lattices in Q_p^n with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake correspondence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces.

63 pages. Fix a gap in the proof of Theorem A.29. A few more details added and exposition improved

References in corpus (6)

• A guide to the reduction modulo p of Shimura varieties
• Rapoport-Zink spaces for spinor groups
• An introduction to affine Grassmannians and the geometric Satake equivalence
• Cycles on Shimura varieties via geometric Satake
• The global structure of moduli spaces of polarized p-divisible groups
• The dimension of affine Deligne-Lusztig varieties in the affine Grassmannian of unramified groups

Cited by in corpus (5)

• Rapoport-Zink spaces for spinor groups
• An introduction to affine Grassmannians and the geometric Satake equivalence
• Stratifications and foliations for good reductions of Shimura varieties of Hodge type
• Hecke algebras and $p$-adic groups
• Connected components of closed affine Deligne-Lusztig varieties