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# Spencer Leslie – Geometric Methods in Representation Theory Seminar

## January 25, 2019 @ 4:00 pm - 5:00 pm

**Title:** *Parity sheaves and Smith theory*

**Abstract: **Parity sheaves are a topologically-defined class of sheaves on a variety with many important connections to modular representation theory. In this talk, we discuss connections between parity sheaves on a variety X endowed with the action of a finite cyclic group of order p and parity sheaves on the fixed-point set. For this we use Smith theory, which gives a localization functor for actions of finite cyclic groups.The key idea is to define a good notion of parity sheaf in an intermediate localized category. In the context of the geometric Satake equivalence, this gives a geometric construction of the Frobenius-contraction functor on tilting modules.