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Journal Articles Publications mathematiques de l' IHES Year : 2022

Smith-Treumann theory and the linkage principle

Abstract

In this paper 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 p-canonical basis, valid in all blocks and in all characteristics.
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Dates and versions

hal-02570416 , version 1 (12-05-2020)

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Simon Riche, Geordie Williamson. Smith-Treumann theory and the linkage principle. Publications mathematiques de l' IHES, 2022, 136, pp.225-292. ⟨hal-02570416⟩
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