Number Theory Seminar: Sarah Diana Meier (University of Bielefeld)
The Right Derived Functors of Ordinary Parts
Emerton's Ordinary Parts functor $Ord$ plays an important role in the theory of mod $p$ representations of $p$-adic reductive groups. The right derived functors of $Ord$ are conjectured by Emerton to be given in terms of group cohomology. In this talk I will discuss a proof of a variant of this conjecture. A key step in this proof is a comparison between certain compact and parabolic inductions. In addition, I will present an explicit description of the right adjoint to parabolic induction (a functor closely related to $Ord$) and deduce a version of Second Adjointness in the mod $p$ setting. This is based on joint work with Manuel Hoff, Michael Spieß and Claudius Heyer
