Algebraic Geometry Seminar

We will focus on two kinds of spherical varieties, the L-monoid and the affine closure of $G/U$ for a connected reductive group $G$ and $U$ its unipotent radical. We will first explain the joint work of the speaker with B.C. Ngô and Y. Sakellaridis which gives a way to construct geometrically unramified local L-factors. Nevertheless, the geometric situation is nicely defined only globally as it is also the case for the affine closure of $G/U$. Locally, we need to consider arc spaces of these spherical varieties which are infinite dimensional and for which there was no theory of perverse sheaves on it. We will then explain the recent work of the speaker with D. Kazhdan which enables to construct such objects and compare it with the global ones.