Speaker: Dennis Gaitsgory (MPI Bonn)

Title: Algebro-geometric version of the Fargues-Scholze Bun_G

Abstract: I’ll describe an ongoing project, joint with Arnaud Eteve, Alain
Genestier and Vincent Lafforgue. We start with an algebro-geometric
incarnation of the Fargues-Scholze D(Bun_G), given by the category
of sheaves on the loop group equivariant with respect to Frobenius-
twisted conjugacy, and our goal is to define on it a ‘spectral’ action
of QCoh of the stack of arithmetic local systems. This is achieved
by a fusion procedure. In the process one has to resolve difficul-
ties associated with taking nearby cycles along a multi-dimensional base.