Unramified cohomology and Witt groups of anisotropic Pfister quadrics

Sujatha, R.

doi:10.1090/S0002-9947-97-01940-5

Unramified cohomology and Witt groups of anisotropic Pfister quadrics
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by R. Sujatha

Trans. Amer. Math. Soc. 349 (1997), 2341-2358

DOI: https://doi.org/10.1090/S0002-9947-97-01940-5

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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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