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Seminars

Seminar in Representation Theory

Character sheaves on tori over local fields

2024/12/19 (Thu.) 12:45~13:45
  • Date : 2024/12/19 (Thu.) 12:45~13:45
  • Location : Seminar Room 617, Institute of Mathematics (NTU Campus)
  • Speaker : Saniya Wagh (Tata Institute of Fundamental Research)
  • Abstract : Let \(T\) be a torus over a complete discrete-valued field with an algebraically closed residue field. We obtain a connected commutative pro-algebraic group denoted by \(L^+ T\) by applying the Greenberg functor to the connected N'eron model of \(T\). In this talk, we look at the multiplicative local systems (character sheaves) on \(L^+ T\). We establish a canonical isomorphism between the abelian group of character sheaves on \(L^+ T\) and the inertial local Langlands parameters. We then relate this isomorphism to the classical local Langlands correspondence for tori using the sheaf-function correspondence for pro-algebraic groups. This is joint work with Tanmay Deshpande.
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