by Bruno Kahn, Markus Rost, and R. Sujatha (41 pages)
Amer. J. Math. 120 (1998), no. 4, 841-891.
Let F be a field of characteristic not 2 and X be a quadric over F. In this paper, we study the kernel and cokernel of the natural map from the Galois cohomology of F, more precisely Hi(F,Q/Z(i-1)), to the corresponding unramified cohomology of the function field of X.
In particular we show for i=4: The kernel is generated by symbols if dim X > 2, has order at most 2 if dim X > 6 and is trivial if dim X > 14. The cokernel has order at most 4 if dim X > 4 and is trivial for dim X > 10.
These results have applications to the unramified Witt ring of F(X).
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