LEADER 04426nam 22006855 450 001 996466771403316 005 20200706122413.0 010 $a3-540-40990-4 024 7 $a10.1007/b94827 035 $a(CKB)1000000000230942 035 $a(SSID)ssj0000323485 035 $a(PQKBManifestationID)11247947 035 $a(PQKBTitleCode)TC0000323485 035 $a(PQKBWorkID)10299887 035 $a(PQKB)11339343 035 $a(DE-He213)978-3-540-40990-8 035 $a(MiAaPQ)EBC6283624 035 $a(MiAaPQ)EBC5584866 035 $a(Au-PeEL)EBL5584866 035 $a(OCoLC)56338005 035 $a(PPN)155187511 035 $a(EXLCZ)991000000000230942 100 $a20121227d2004 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aGeometric Methods in the Algebraic Theory of Quadratic Forms$b[electronic resource] $eSummer School, Lens, 2000 /$fby Oleg T. Izhboldin, Bruno Kahn, Nikita A. Karpenko, Alexander Vishik ; edited by Jean-Pierre Tignol 205 $a1st ed. 2004. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2004. 215 $a1 online resource (XIV, 198 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1835 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-20728-7 320 $aIncludes bibliographical references. 327 $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). 330 $aThe geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the renewal of the theory by Pfister in the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes - an introduction to motives of quadrics by Alexander Vishik, with various applications, notably to the splitting patterns of quadratic forms under base field extensions; - papers by Oleg Izhboldin and Nikita Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields which carry anisotropic quadratic forms of dimension 9, but none of higher dimension; - a contribution in French by Bruno Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties. Most of the material appears here for the first time in print. The intended audience consists of research mathematicians at the graduate or post-graduate level. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1835 606 $aNumber theory 606 $aAlgebraic geometry 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aNumber theory. 615 0$aAlgebraic geometry. 615 14$aNumber Theory. 615 24$aAlgebraic Geometry. 676 $a512.7/4 700 $aIzhboldin$b Oleg T$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478892 702 $aKahn$b Bruno$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aKarpenko$b Nikita A$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVishik$b Alexander$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTignol$b Jean-Pierre$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466771403316 996 $aGeometric methods in the algebraic theory of quadratic forms$9262676 997 $aUNISA