# Motivic cohomology and unramified cohomology of quadrics

Journal of the European Mathematical Society (2000)

- Volume: 002, Issue: 2, page 145-177
- ISSN: 1435-9855

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topKahn, 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 -

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