On Second Adjointness for mod p Representations

Abstract: The parabolic induction functor for smooth representations admits the Jacquet functor as a left adjoint. For complex representations it is a deep result of Bernstein, called Second Adjointness, that the Jacquet functor for the opposite parabolic is (up to a twist) also right adjoint to parabolic induction. A similar result is also known for mod ℓ≠p representations, yet for mod p representations the story is a bit more intricate. Due to recent work of Hoff–Meier–Spieß the (derived) right adjoint of parabolic induction is now fairly well understood. In this talk I will explain Second Adjointness for smooth mod p representations, which is joint work with Manuel Hoff, Sarah Meier and Michael Spieß.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

KIAS HCMC Algebra Seminar

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