The Arason invariant and mod 2 algebraic cycles

Esnault, Hélène ¹   ; Kahn, Bruno ²   ; Levine, Marc ³   ; Viehweg, Eckart ¹

¹ FB6, Mathematik, Universität Essen, D-45117 Essen, Germany
² Institut de Mathématiques de Jussieu, Université Paris 7, Case 7012, 75251 Paris Cedex 05, France
³ Department of Mathematics, Northeastern University, Boston, Massachusetts 02115

Journal of the American Mathematical Society, Tome 11 (1998) no. 1, pp. 73-118

Résumé

Let $k$ be a field, $X$ over $k$ a smooth variety with function field $K$ and $E$ a quadratic vector bundle over $X$. Assuming that the generic fibre $q$ of $E$ is in $I^3K\subset W(K)$, we compute the image of its Arason invariant \[ e^3(q)\in H^0(X,{\mathcal H}_{\mathrm {\acute {e}t}}^3({\mathbb Z}/2))\] in $CH^2(X)/2$ by the $d_2$ differential of the Bloch-Ogus spectral sequence. This gives an obstruction to $e^3(q)$ being a global cohomology class.

Détail

DOI : 10.1090/S0894-0347-98-00248-3

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