Integrality of G-local systems

2022.02.14

Date: 2021-11-17 (16:30 ~ 18:00)
Location: Online(zoom)

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 $G L_{n}$ . Surprisingly, the main tools used in the proof (for general $G$ and $G L_{n}$ ) are the work of L. Lafforgue on the Langlands program for curves over function fields, and work of Drinfeld on companions of $ℓ$ -adic sheaves. The major differences between general $G$ and $G L_{n}$ 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.

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Integrality of G-local systems