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NON-INJECTIVITY OF THE MAP FROM THE WITT GROUP OF A VARIETY TO THE WITT GROUP OF ITS FUNCTION FIELD

Published online by Cambridge University Press:  21 July 2003

Burt Totaro
Burt Totaro
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK (b.totaro@dpmms.cam.ac.uk)
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Abstract

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We exhibit a smooth complex affine 5-fold whose Witt group of quadratic forms does not inject into the Witt group of its function field. The dimension 5 is the smallest possible. The example depends on relating Witt groups, mod 2 Chow groups, and Steenrod operations.

AMS 2000 Mathematics subject classification: Primary 19G12. Secondary 19E15

Keywords

Witt groupChow groupSteenrod operationunramified cohomology
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 2 , Issue 3 , July 2003 , pp. 483 - 493
Copyright
2003 Cambridge University Press