On the Grothendieck–Serre conjecture for classical groups

Eva Bayer-Fluckiger; Uriya A. First; Raman Parimala

doi:10.1112/jlms.12651

On the Grothendieck–Serre conjecture for classical groups

Eva Bayer-Fluckiger, Uriya A. First, Raman Parimala

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	2884-2926
Number of pages	43
Journal	Journal of the London Mathematical Society
Volume	106
Issue number	4
DOIs	https://doi.org/10.1112/jlms.12651
State	Published - Dec 2022

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© 2022 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.

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General Mathematics

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10.1112/jlms.12651

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On the Grothendieck–Serre conjecture for classical groups

Abstract

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