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Mathematische Annalen

, Volume 370, Issue 1–2, pp 309–329 | Cite as

Cohomological invariants for quadratic forms over local rings

  • Jeremy Allen JacobsonEmail author
Article

Abstract

Let A be local ring in which 2 is invertible and let n be a non-negative integer. We show that the nth cohomological invariant of quadratic forms is a well-defined homomorphism from the nth power of the fundamental ideal in the Witt ring of A to the degree n étale cohomology of A with mod 2 coefficients, which is surjective and has kernel the (\(\hbox {n}+1\))th power of the fundamental ideal. This is obtained by proving the Gersten conjecture for Witt groups in an important mixed-characteristic case.

Mathematics Subject Classification

Primary 11E08 Secondary 14F20 

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© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Emory UniversityAtlantaUSA

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