A toy model for the Drinfeld-Lafforgue shtuka construction

Abstract

The goal of this paper is to provide a categorical framework that leads to the definition of shtukas \`a la Drinfeld and of excursion operators \`a la V. Lafforgue. We take as the point of departure the Hecke action of Rep(G^L) on the category Shv(Bun_G) of sheaves on Bun_G, and also the endofunctor of the latter category, given by the action of the geometric Frobenius. The shtuka construction will be obtained by applying (various versions of) categorical trace.