Grothendieck-Serre Conjecture for Quasi-split Reductive Groups
Algebraic Geometry
2021-12-01 v2 Representation Theory
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.
Cite
@article{arxiv.2110.14745,
title = {Grothendieck-Serre Conjecture for Quasi-split Reductive Groups},
author = {Neeraj Deshmukh and Amit Hogadi and Suraj Yadav},
journal= {arXiv preprint arXiv:2110.14745},
year = {2021}
}
Comments
There is a gap in the proof of Theorem 1.2 which, as yet, we cannot resolve. We thank K\k{e}stutis \v{C}esnavi\v{c}ius, Roman Federov and Sean Cotner for pointing out the gap in the proof