Grothendieck-Serre Conjecture for Quasi-split Reductive Groups

Abstract

We prove the Grothendieck-Serre conjecture for quasi-split reductive groups schemes. Our method involves reducing to the Borel subgroup in order to conclude the result from purity for tori and the structure theorem for unipotent radicals of parabolic subgroups in a reductive group.

arXiv commentThere is a gap in the proof of Theorem 1.2 which, as yet, we cannot resolve. We thank Kęstutis Česnavičius, Roman Federov and Sean Cotner for pointing out the gap in the proof