Mathematics Seminar
Date: Monday, 9 December 2024
Time: 11.00 AM
Venue: LH 801
Grothendieck-Serre Conjecture for Parahoric Group Schemes
Arnab Kundu
University of Toronto.
09-12-24

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Abstract

Bruhat-Tits' parahoric group schemes, denoted by P, are certain non-reductive integral O_K​-models of reductive groups G, defined over p-adic local fields K, and are associated with maximal compact subgroups of G(K). Extending the work of Balaji–Seshadri and Pappas–Rapoport, we demonstrate that these group schemes are reductive up to a finite, generically-Galois cover of O_K​. Leveraging this result, we show that generically trivial P-torsors over O are trivial in several important special cases. This is joint work with Balaji, Česnavičius, Elmanto and Youcis