Seminar on Arithmetic Geometry

Let $G$ be a split reductive group, $X$ a smooth proper curve over a finite field and $x \in X$ a place. Let $F_x$ the completion of the function field of $X$ at $x$. In this setting, Lafforgue and Genestier have constructed a semisimple local Langlands correspondence for $G(F_x)$ by geometric methods. In another direction, DeBacker and Reeder have constructed the depth $0$ part of a local Langlands correspondence by representation theoretic methods. In this talk, I will discuss some compatibility statement between the two constructions and explain the connection to global chtoucas over $X$.

Arnaud Eteve (ENS, Paris)

Zoom (Meeting-ID: 635 7328 0984, Password: smallest six digit prime)