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Unramified cohomology and Witt groups of anisotropic Pfister quadrics

Author: R. Sujatha
Journal: Trans. Amer. Math. Soc. 349 (1997), 2341-2358
MSC (1991): Primary 11E70; Secondary 13K05, 12G05
MathSciNet review: 1422911
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Abstract: The unramified Witt group of an anisotropic conic over a field $k$, with $char~k \neq 2$, defined by the form $\langle 1,-a,-b\rangle $ is known to be a quotient of the Witt group $W(k)$ of $k$ and isomorphic to $W( {k})/\langle 1,-a,-b,ab \rangle W( {k})$. We compute the unramified cohomology group $H^{3}_{nr}{k({C})}$, where $C$ is the three dimensional anisotropic quadric defined by the quadratic form $\langle 1,-a,-b,ab,-c\rangle $ over $k$. We use these computations to study the unramified Witt group of $C$.

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Additional Information

R. Sujatha
Affiliation: Department of Mathematics, Ohio State University, 231 W 18th Avenue, Columbus, Ohio 43210 \indent{Permanent address}: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India

Keywords: Pfister forms, unramified cohomology, ├ętale cohomology
Received by editor(s): November 7, 1995
Dedicated: Dedicated to my father on his sixtieth birthday
Article copyright: © Copyright 1997 American Mathematical Society

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