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Geometric Methods in the Algebraic Theory of Quadratic Forms

Summer School, Lens, 2000

  • Book
  • © 2004

Overview

Authors:
  1. Oleg T. Izhboldin
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  2. Bruno Kahn
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  3. Nikita A. Karpenko
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  4. Alexander Vishik
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Editors:
  1. Jean-Pierre Tignol
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1835)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Cohomologie non ramifiée des quadriques

    • Bruno Kahn
    Pages 1-23

  3. Motives of Quadrics with Applications to the Theory of Quadratic Forms

    • Alexander Vishik
    Pages 25-101

  4. Motives and Chow Groups of Quadrics with Application to the u-invariant (after Oleg Izhboldin)

    • Nikita A. Karpenko
    Pages 103-129

  5. Virtual Pfister Neighbors and First Witt Index

    • Oleg T. Izhboldin
    Pages 131-142

  6. Some New Results Concerning Isotropy of Low-dimensional Forms

    • Oleg T. Izhboldin
    Pages 143-150

  7. Izhboldin’s Results on Stably Birational Equivalence of Quadrics

    • Nikita A. Karpenko
    Pages 151-183

  8. Appendix: My Recollections About Oleg Izhboldin

    • Alexander S. Merkurjev
    Pages 185-187

  9. Back Matter

    Pages 189-190
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Keywords

About this book

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin and N. Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields with u-invariant 9, and a contribution in French by B. Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.

Bibliographic Information

  • Book Title: Geometric Methods in the Algebraic Theory of Quadratic Forms

  • Book Subtitle: Summer School, Lens, 2000

  • Authors: Oleg T. Izhboldin, Bruno Kahn, Nikita A. Karpenko, Alexander Vishik

  • Editors: Jean-Pierre Tignol

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b94827

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2004

  • Softcover ISBN: 978-3-540-20728-3Published: 19 February 2004

  • eBook ISBN: 978-3-540-40990-8Published: 07 February 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 198

  • Topics: Number Theory, Algebraic Geometry

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