Motivicity of Rigid G-Local Systems on Curves

A natural problem in the study of local systems on complex varieties is to characterize those that arise in a family of varieties. We refer to such local systems as motivic. While a classification of motivic local systems is evidently out of reach, Simpson conjectured that for a reductive group G, rigid G-local systems with suitable finiteness conditions at infinity are motivic. This was proven for curves when G = GL_n by Katz, who classified such rigid local systems. In this talk, we discuss our generalization of Katz’s theorem to a general reductive group. Our proof goes through the (tamely ramified) categorical geometric Langlands program in characteristic zero.