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The Arason invariant and mod 2 algebraic cycles
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by Hélène Esnault, Bruno Kahn, Marc Levine and Eckart Viehweg PDF
J. Amer. Math. Soc. 11 (1998), 73-118 Request permission

Abstract:

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.
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Additional Information
  • Hélène Esnault
  • Affiliation: FB6, Mathematik, Universität Essen, D-45117 Essen, Germany
  • MR Author ID: 64210
  • 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
  • MR Author ID: 113315
  • Email: marc@neu.edu
  • Eckart Viehweg
  • Affiliation: FB6, Mathematik, Universität Essen, D-45117 Essen, Germany
  • Email: viehweg@uni-essen.de
  • 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 1998 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 11 (1998), 73-118
  • MSC (1991): Primary 11E81; Secondary 55R40
  • DOI: https://doi.org/10.1090/S0894-0347-98-00248-3
  • MathSciNet review: 1460391