8th November: Lukas Kofler

Title:The plectic Langlands-Rapoport conjecture

Abstract: The Langlands-Rapoport conjecture predicts the number of points modulo p of a Shimura variety. We will explain why Shimura varieties, and this conjecture in particular, are an important tool for the Langlands programme. We will first look at the case of modular curves. Then we will outline the general formalism, which involves motives, gerbes, and affine Deligne-Lusztig varieties. The plectic conjecture of Nekovar and Scholl predicts that certain Shimura varieties are equipped with additional structure of motivic origin. This leads to a refinement of the Langlands-Rapoport conjecture. We will sketch a possible proof strategy.