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020 _a9783540409908
_9978-3-540-40990-8
024 7 _a10.1007/b94827
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
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082 0 4 _a512.7
_223
100 1 _aIzhboldin, Oleg T.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aGeometric Methods in the Algebraic Theory of Quadratic Forms
_h[electronic resource] :
_bSummer School, Lens, 2000 /
_cby Oleg T. Izhboldin, Bruno Kahn, Nikita A. Karpenko, Alexander Vishik ; edited by Jean-Pierre Tignol.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2004.
300 _aXIV, 198 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1835
505 0 _aCohomologie 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).
520 _aThe 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.
650 0 _aNumber theory.
650 0 _aGeometry, algebraic.
650 1 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
700 1 _aKahn, Bruno.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aKarpenko, Nikita A.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aVishik, Alexander.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aTignol, Jean-Pierre.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540207283
776 0 8 _iPrinted edition:
_z9783662177747
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1835
856 4 0 _uhttps://doi.org/10.1007/b94827
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10920
_d10920