Motivic cohomology and unramified cohomology of quadrics

Kahn, Bruno, and Sujatha, R.. "Motivic cohomology and unramified cohomology of quadrics." Journal of the European Mathematical Society 002.2 (2000): 145-177. <http://eudml.org/doc/277321>.

@article{Kahn2000,
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 $\le 4$ and $\ge 11$. 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.},
author = {Kahn, Bruno, Sujatha, R.},
journal = {Journal of the European Mathematical Society},
keywords = {unramified cohomology; Pfister quadric; unramified Witt ring; Voevodsky’s motivic cohomology; quadratic forms; function field of a quadric; Pfister forms; Pfister neighbor; Galois cohomology; unramified cohomology; Voevodsky's motivic cohomology; Chow group},
language = {eng},
number = {2},
pages = {145-177},
publisher = {European Mathematical Society Publishing House},
title = {Motivic cohomology and unramified cohomology of quadrics},
url = {http://eudml.org/doc/277321},
volume = {002},
year = {2000},
}

TY - JOUR
AU - Kahn, Bruno
AU - Sujatha, R.
TI - Motivic cohomology and unramified cohomology of quadrics
JO - Journal of the European Mathematical Society
PY - 2000
PB - European Mathematical Society Publishing House
VL - 002
IS - 2
SP - 145
EP - 177
AB - 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 $\le 4$ and $\ge 11$. 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.
LA - eng
KW - unramified cohomology; Pfister quadric; unramified Witt ring; Voevodsky’s motivic cohomology; quadratic forms; function field of a quadric; Pfister forms; Pfister neighbor; Galois cohomology; unramified cohomology; Voevodsky's motivic cohomology; Chow group
UR - http://eudml.org/doc/277321
ER -