Affine Grassmannians and the geometric Satake in mixed characteristic

2014/07/31 by Xinwen Zhu, Zhu, Xinwen · 7 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.AG #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1407.8519

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

openalex publication_date 2014/07/31 · arxiv created 2016/07/20 · arxiv updated 2016/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We endow the set of lattices in Q_pⁿ 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.

Citations

• A bar operator for involutions in a Coxeter group
• A guide to the reduction modulo p of Shimura varieties

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• Lifting Deligne-Lusztig Reduction and Geometric Coxeter Type Elements
• An introduction to affine Grassmannians and the geometric Satake equivalence
• Arithmetic and Geometric Langlands Program

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