1. Smith-Treumann theory and the linkage principle
- Author
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Riche, Simon, Williamson, Geordie, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Université Clermont Auvergne [2017-2020] (UCA [2017-2020]), The University of Sydney, European Project: 677147,H2020,ERC-2015-STG,ModRed(2016), and European Project: RedLang
- Subjects
Mathematics - Algebraic Geometry ,[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] ,FOS: Mathematics ,Algebraic Topology (math.AT) ,Mathematics - Algebraic Topology ,Representation Theory (math.RT) ,Mathematics::Representation Theory ,Algebraic Geometry (math.AG) ,Mathematics - Representation Theory - Abstract
We apply Treumann's "Smith theory for sheaves" in the context of the Iwahori--Whittaker model of the Satake category. We deduce two results in the representation theory of reductive algebraic groups over fields of positive characteristic: (a) a geometric proof of the linkage principle; (b) a character formula for tilting modules in terms of the $\ell$-canonical basis, valid in all blocks and in all characteristics., 52 pages, revised version, to appear in Publ. IHES
- Published
- 2020