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Generic points of quadrics and Chow groups

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Abstract

In this article we study the sufficient conditions for the k̅-defined element of the Chow group of a smooth variety to be k-rational (defined over k). For 0-cycles this question was addressed earlier. Our methods work for cycles of arbitrary dimension. We show that it is sufficient to check this property over the generic point of a quadric of sufficiently large dimension. Among the applications one should mention the uniform construction of fields with all known u-invariants.

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  1. Institute for Information Transmisson Problems, R.A.S., Bolshoj Karetnyj per., 19, Moscow, 127994, Russia

    A. Vishik

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  1. A. Vishik
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Vishik, A. Generic points of quadrics and Chow groups. manuscripta math. 122, 365–374 (2007). https://doi.org/10.1007/s00229-007-0074-6

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  • DOI: https://doi.org/10.1007/s00229-007-0074-6

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