On the Gersten conjecture for hermitian Witt groups

TL;DR

This paper proves the exactness of the hermitian Gersten-Witt complex for certain Azumaya algebras with involution over regular local rings, advancing understanding in algebraic K-theory and quadratic forms.

Contribution

It establishes the exactness of the hermitian Gersten-Witt complex for Azumaya algebras with involution over specific regular local rings, extending previous results.

Findings

Hermitian Gersten-Witt complex is exact for these algebras.

Results apply to rings essentially smooth over a field or a DVR.

Advances understanding of quadratic forms and algebraic K-theory.

Abstract

We prove that the hermitian Gersten-Witt complex is exact for Azumaya algebras with involution of the first- or second kind over a regular local ring, which is essentially smooth over a field, or over a discrete valuation ring.