A zero theorem for the transfer of coherent Witt groups

✍ Scribed by Stefan Gille; Jens Hornbostel

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 173 KB
• Volume: 278
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310274

✦ Synopsis

Abstract

Let R be a Gorenstein ring of finite Krull dimension and t ∈ R a regular element. We show that if the quotient map R → R/Rt has a flat splitting then the transfer morphism of coherent Witt groups Tr~(R/Rt)/R~ : $ \widetilde W^{i} $(R/Rt) → $ \widetilde W^{i+1} $(R) is zero for all i ∈ ℤ. As an application we give another proof of the Gersten conjecture for Witt groups in the case of regular semilocal rings essentially of finite type over a field of characteristic not 2. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)