Unramified cohomology of quadrics, I

Sujatha, R. ; Rost, Markus ; Kahn, Bruno (1998) Unramified cohomology of quadrics, I American Journal of Mathematics, 120 (4). pp. 841-891. ISSN 0002-9327

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Official URL: http://muse.jhu.edu/login?uri=/journals/american_j...

Related URL: http://dx.doi.org/10.1353/ajm.1998.0029

Abstract

Given a quadric X over a field F of characteristic ≠ 2, we compute the kernel and cokernel of the natural map in degree 4 from the mod 2 Galois cohomology of F to the unramified mod 2 cohomology of F(X), when dim X > 10 and in several smaller-dimensional cases. Applications of these results to real quadrics and to the unramified Witt ring are given.

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