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.
Bibliographical noteFunding 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.
© 2022 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.
ASJC Scopus subject areas
- Mathematics (all)