# Motivic cohomology and unramified cohomology of quadrics

Motivic cohomology and unramified cohomology of quadrics 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 ≤4 and ≥11. Here we deal with the remaining dimensions between 5 and 10. 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. For most of the paper we have to assume that the ground field has characteristic 0, because we use Voevodsky’s motivic cohomology. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

# Motivic cohomology and unramified cohomology of quadrics

, Volume 2 (2) – Jun 1, 2000
33 pages

Publisher
Springer Journals
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970000015
Publisher site
See Article on Publisher Site

### Abstract

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 ≤4 and ≥11. Here we deal with the remaining dimensions between 5 and 10. 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. For most of the paper we have to assume that the ground field has characteristic 0, because we use Voevodsky’s motivic cohomology.

### Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Jun 1, 2000