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

Abstract: I’ll describe on a going project, joint with Arnaud Eteve, Alain Genestier and Vincent Lafforgue. We start with an algebra-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 difficulties associated with taking nearby cycles along a multi-dimensional base.

Location: UQAM PK-5675