# Simon Riche: Smith-Treumann theory and representations of reductive algebraic groups

**Time: **
Wed 2021-06-09 13.15 - 14.15

**Location: **
Zoom, meeting ID: 685 0671 8075

**Lecturer: **
Simon Riche

### Abstract

Given a prime number *p* and a variety *X* endowed with an action of the cyclic group of order *p*, Smith theory is a "localization theory" that relates the cohomology of *X* with coefficients in a field of characteristic *p* and that the fixed points of the action. A few years ago Treumann developed a sheaf-theoretic version of this theory, now called Smith-Treumann theory, which found applications to Langlands functoriality in work of Treumann-Venkatesh and Feng. In this talk I will present a different application of this theory, obtained in joint work with G. Williamson, in the framework of representations of reductive algebraic groups in characteristic *p*. Here, using the Geometric Satake Equivalence of Mirkovic-Vilonen, we use Smith-Treumann theory to obtain a geometric proof of the linkage principle, and of a character formula for indecomposable tilting modules that we had conjectured a few years ago. This talk will be based on
arxiv.org/abs/2003.08522
.

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