On the Gersten conjecture for hermitian Witt groups

2022/01/26 by Stefan Gille, Gille, Stefan, Ivan Panin +1
Mathematics · #11E70 #11E81 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2201.10715

openalex publication_date 2022/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On The Gersten-Witt Complex of an Azumaya Algebra with Involution
• An 8-Periodic Exact Sequence of Witt Groups of Azumaya Algebras with Involution
• Pfister's local-global principle for Azumaya algebras with involution
• Gersten's conjecture
• Local Gersten's conjecture for regular system of parameters