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Algebra Seminar

Algebraic groups with good reduction and unramified cohomology

Igor Rapinchuk -- Michigan State

Location:  Hill 525
Date & time: Wednesday, 31 October 2018 at 2:00PM - 3:00PM

Abstract:  Let G be an absolutely almost simple algebraic group over a field K, which we assume to be equipped with a natural set V of discrete valuations. In this talk, our focus will be on the K-forms of G that have good reduction at all v in V . When K is the fraction field of a Dedekind domain, a similar question was considered by G. Harder; the case where K=Q and V is the set of all p-adic places was analyzed in detail by B.H. Gross and B. Conrad. I will discuss several emerging results in the higher-dimensional situation, where K is the function field k(C) of a smooth geometrically irreducible curve C over a number field k, or even an arbitrary finitely generated field.

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