Journal of the American Mathematical Society

Author(s): Hélène Esnault; Bruno Kahn; Marc Levine; Eckart Viehweg
Journal: J. Amer. Math. Soc. 11 (1998), 73-118.
MSC (1991): Primary 11E81; Secondary 55R40
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Abstract: Let $k$

be a field, $X$

over

a smooth variety with function field $K$

and

a quadratic vector bundle over $X$

. Assuming that the generic fibre $q$

is in $I^3K\subset W(K)$ , we compute the image of its Arason invariant

$\begin{displaymath}e^3(q)\in H^0(X,{\mathcal H}_{\mathrm{\acute{e}t}}^3({\mathbb Z}/2))\end{displaymath}$

by the

differential of the Bloch-Ogus spectral sequence. This gives an obstruction to $e^3(q)$

being a global cohomology class.

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Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 11E81, 55R40

Hélène Esnault
Affiliation: FB6, Mathematik, Universität Essen, D-45117 Essen, Germany
Email: esnault@uni-essen.de

Bruno Kahn
Affiliation: Institut de Mathématiques de Jussieu, Université Paris 7, Case 7012, 75251 Paris Cedex 05, France
Email: kahn@math.jussieu.fr

Marc Levine
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email: marc@neu.edu

Eckart Viehweg
Affiliation: FB6, Mathematik, Universität Essen, D-45117 Essen, Germany
Email: viehweg@uni-essen.de

DOI: 10.1090/S0894-0347-98-00248-3
PII: S 0894-0347(98)00248-3
Received by editor(s): September 13, 1996
Received by editor(s) in revised form: July 28, 1997
Additional Notes: This research was partially supported by the DFG Forschergruppe ``Arithmetik und Geometrie''; the second and third author gratefully acknowledge its hospitality.
Copyright of article: Copyright 1998, American Mathematical Society

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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