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Lecture Notes in Mathematics

Geometric Methods in the Algebraic Theory of Quadratic Forms

Summer School, Lens, 2000

Authors: Izhboldin, O.T., Kahn, B., Karpenko, N.A., Vishik, A.

Editors: Tignol, Jean-Pierre (Ed.)

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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 renewal of the theory by Pfister in 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 Alexander Vishik, with various applications, notably to the splitting patterns of quadratic forms under base field extensions;
- papers by Oleg Izhboldin and Nikita Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields which carry anisotropic quadratic forms of dimension 9, but none of higher dimension;
- a contribution in French by Bruno Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.

Most of the material appears here for the first time in print. The intended audience consists of research mathematicians at the graduate or post-graduate level.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-540-40990-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA in USD
  • ISBN 978-3-540-20728-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Methods in the Algebraic Theory of Quadratic Forms
Book Subtitle
Summer School, Lens, 2000
Authors
Editors
  • Jean-Pierre Tignol
Series Title
Lecture Notes in Mathematics
Series Volume
1835
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-40990-8
DOI
10.1007/b94827
Softcover ISBN
978-3-540-20728-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 198
Topics