MATH Seminar

Title: Local-global principles for reductive groups over finitely generated fields
Seminar: Algebra
Speaker: Igor Rapinchuk of Michigan State University
Contact: Andrew Kobin, andrew.jon.kobin@emory.edu
Date: 2023-10-03 at 4:00PM
Venue: MSC N302
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Abstract: One of the major results in the arithmetic theory of algebraic groups is the validity of the cohomological local-global (or Hasse) principle for simply-connected and adjoint semisimple groups over number fields. Over the last several years, there has been growing interest in studying Hasse principles for reductive groups over arbitrary finitely generated fields with respect to suitable sets of discrete valuations. In particular, we have conjectured that for divisorial sets, the corresponding Tate-Shafarevich set, which measures the deviation from the local-global principle, should be finite for all reductive groups. I will report on recent progress on this conjecture, focusing in particular on the case of algebraic tori as well as on connections to groups with good reduction. This talk is based on joint work with V. Chernousov and A. Rapinchuk.