Geometric methods in the algebraic theory of quadratic forms : summer school, Lens, 2000
Author(s)
Bibliographic Information
Geometric methods in the algebraic theory of quadratic forms : summer school, Lens, 2000
（Lecture notes in mathematics, 1835）
Springer, c2004
Available at / 61 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||183504003458
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:512.7/IZ22080001888
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Note
In English, with one contribution in French
Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of Contents
Cohomologie non ramifiee des quadriques (B. Kahn).- Motives of Quadrics with Applications to the Theory of Quadratic Forms (A. Vishik).- Motives and Chow Groups of Quadrics with Applications to the u-invariant (N.A. Karpenko after O.T. Izhboldin).- Virtual Pfister Neigbors and First Witt Index (O.T. Izhboldin).- Some New Results Concerning Isotropy of Low-dimensional Forms (O.T. Izhboldin).- Izhboldin's Results on Stably Birational Equivalence of Quadrics (N.A. Karpenko).- My recollections about Oleg Izhboldin (A.S. Merkurjev).
by "Nielsen BookData"