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
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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