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Fields of u-Invariant 2r + 1

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Algebra, Arithmetic, and Geometry

Part of the book series: Progress in Mathematics ((PM,volume 270))

Summary

In this article we provide a uniform construction of fields with all known u-invariants. We also obtain the new values for the u-invariant: 2r + 1, for r > 3. The main tools here are the new discrete invariant of quadrics (so-called elementary discrete invariant), and the methods of [14] (which permit one to reduce the questions of rationality of elements of the Chow ring over the base field to that over bigger fields, the generic point of a quadric).

2000 Mathematics Subject Classifications: 11E04, 14C15, 14C35, 55S05, 55N22

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Alexander Vishik

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  1. Alexander Vishik
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Correspondence to Alexander Vishik .

Editor information

Editors and Affiliations

  1. Courant Inst. Mathematical, New York University, Mercer St. 251, New York, 10012, USA

    Yuri Tschinkel

  2. Eberly College of Science, Pennsylvania State University, University Park, 16802, USA

    Yuri Zarhin

Additional information

To my teacher Yuri Ivanovich Manin with gratitude

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Vishik, A. (2009). Fields of u-Invariant 2r + 1. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 270. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4747-6_22

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