TY - JOUR
T1 - On the Grothendieck–Serre conjecture for classical groups
AU - Bayer-Fluckiger, Eva
AU - First, Uriya A.
AU - Parimala, Raman
N1 - Funding Information: We are grateful to Stefan Gille and Paul Balmer for several useful correspondences. We also thank the anonymous referees for their comments and suggestions. The third author was partially supported by the NSF grant DMS‐1801951. Publisher Copyright: © 2022 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.
PY - 2022
Y1 - 2022
N2 - We prove some new cases of the Grothendieck–Serre conjecture for classical groups. This is based on a new construction of the Gersten–Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue maps; the complex is shown to be exact when the ring is of dimension (Formula presented.) (or (Formula presented.), with additional hypotheses on the algebra with involution). Note that we do not assume that the ring contains a field.
AB - We prove some new cases of the Grothendieck–Serre conjecture for classical groups. This is based on a new construction of the Gersten–Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue maps; the complex is shown to be exact when the ring is of dimension (Formula presented.) (or (Formula presented.), with additional hypotheses on the algebra with involution). Note that we do not assume that the ring contains a field.
UR - http://www.scopus.com/inward/record.url?scp=85129515435&partnerID=8YFLogxK
U2 - https://doi.org/10.1112/jlms.12651
DO - https://doi.org/10.1112/jlms.12651
M3 - Article
SN - 0024-6107
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
ER -