Speaker
Arnaud Etève
Description
Let $G$ be a reductive group over an algebraic closure of $\mathbb{F}_q$. In a joint work in progress with D. Gaitsgory, A. Genestier and V. Lafforgue, we construct a spectral action on the stack of $G$-isocrystals over $\mathbb{F}_q((t))$. The construction that we propose works in greater generality and not just for the stack of isocrystal, as an example, it also recovers the construction of the central functor of Gaitsgory. The goal of this talk will be to discuss the machinery at play, some examples and consequences.