On the Grothendieck-Serre Conjecture for Classical Groups

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

doi:10.1112/jlms.12651

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arXiv · 1911.07666

On the Grothendieck-Serre Conjecture for Classical Groups

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

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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 $\le 2$ (or $\le 4$, with additional hypotheses on the algebra with involution). Note that we do not assume that the ring contains a field.

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BibTeX RIS

Eva Bayer-Fluckiger, Uriya A. First, Raman Parimala. 2022-04-05. On the Grothendieck-Serre Conjecture for Classical Groups. https://doi.org/10.1112/jlms.12651

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