Integrality of G-local systems

2021-11-17   (16:30 ~ 18:00)

November 17 (Wednesday) 2021, 16:30 – 18:00, Building 108, Room N319

Speaker : Christian Sleek Klevdal (UNIST)

Title : Integrality of G-local systems

Abstract : Simpson conjectured that for a reductive group G, rigid G-local systems on a smooth projective complex variety are integral. I will discuss a proof of integrality for cohomologically rigid G-local systems. This generalizes and is inspired by work of Esnault and Groechenig for GLn. Surprisingly, the main tools used in the proof (for general G and GLn) are the work of L. Lafforgue on the Langlands program for curves over function fields, and work of Drinfeld on companions of -adic sheaves. The major differences between general G and GLn are first to make sense of companions for G-local systems, and second to show that the monodromy group of a rigid G-local system is semisimple. All work is joint with Stefan Patrikis.