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- catalog abstract "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.".
- catalog contributor b13177742.
- catalog contributor b13177743.
- catalog contributor b13177744.
- catalog created "c2004.".
- catalog date "2004".
- catalog date "c2004.".
- catalog dateCopyrighted "c2004.".
- catalog description "Cohomologie non ramifiée 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). .".
- catalog description "Includes bibliographical references and index.".
- catalog 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 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.".
- catalog extent "xiv, 190 p. ;".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540207287 (softcover : acid-free paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1835.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1835".
- catalog issued "2004".
- catalog issued "c2004.".
- catalog language "In English, with one contribution in French.".
- catalog language "eng".
- catalog language "engfre".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 512.7/4 22".
- catalog subject "Algebraic fields.".
- catalog subject "Forms, Pfister.".
- catalog subject "Forms, Quadratic.".
- catalog subject "Geometry, algebraic.".
- catalog subject "Mathematics.".
- catalog subject "Number theory.".
- catalog subject "QA3 .L28 no. 1835 QA243".
- catalog tableOfContents "Cohomologie non ramifiée 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). .".
- catalog title "Geometric methods in the algebraic theory of quadratic forms : Summer school, Lens, 2000 / Oleg T. Izhboldin ... [et al.] ; editor, Jean-Pierre Tignol.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".