Unramified cohomology of quadrics, III, by Bruno Kahn and R. Sujatha

This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension at most 4 and at least 11. Here we deal with the remaining dimensions (between 5 and 10) and get partial results. We also prove that the unramified cohomology of Pfister quadrics (with divisible coefficients) always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real quadrics.

In most of the paper we have to assume that the ground field has characteristic 0, because we use Voevodsky's motivic cohomology.

0221 and 0338 are parts I and II of this series.

Bruno Kahn <kahn@math.jussieu.fr>
R. Sujatha <sujatha@math.tifr.res.in>