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035   $a(EBL)1561563
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035   $a(DE-B1597)447654
035   $a(OCoLC)864551391
035   $a(OCoLC)979758910
035   $a(DE-B1597)9781400850532
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100   $a20190708d2014      fg             0
101 0 $aeng
135   $aurun#---|u||u
181   $ctxt
182   $cc
183   $acr
200 10$aChow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187) /$fClaire Voisin
205   $aCourse Book
210  1$aPrinceton, NJ :$cPrinceton University Press,$d[2014]
210  4$d©2014
215   $a1 online resource (172 p.)
225 0 $aAnnals of Mathematics Studies ;$v211
300   $aDescription based upon print version of record.
311   $a0-691-16050-3 
311   $a1-306-16025-1 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$tPreface --$tChapter One. Introduction --$tChapter Two. Review of Hodge theory and algebraic cycles --$tChapter Three. Decomposition of the diagonal --$tChapter Four. Chow groups of large coniveau complete intersections --$tChapter Five. On the Chow ring of K3 surfaces and hyper-Kähler manifolds --$tChapter Six. Integral coefficients --$tBibliography --$tIndex
330   $aIn this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by Voisin. The book focuses on two central objects: the diagonal of a variety-and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups-as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by Voisin looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.
410  0$aAnnals of Mathematics Studies
606   $aAlgebraic varieties
606   $aDecomposition (Mathematics)
606   $aHomology theory
606   $aMathematics
606   $aAlgebraic varieties
606   $aDecomposition (Mathematics)
606   $aHomology theory
610   $aBloch-Beilinson conjectures.
610   $aCalabi?au hypersurfaces.
610   $aChow groups.
610   $aHodge classes.
610   $aHodge coniveau.
610   $aHodge structures.
610   $aK3 surfaces.
610   $aLefschetz standard conjecture.
610   $aMumford's theorem.
610   $aZ-coefficients.
610   $aabelian varieties.
610   $abirational invariants.
610   $acohomology.
610   $acomplex algebraic varieties.
610   $aconiveau.
610   $acycle classes.
610   $adecomposition isomorphism.
610   $adecomposition.
610   $adense Zariski open set.
610   $adiagonal.
610   $afunctoriality.
610   $ageneralized Bloch conjecture.
610   $ageneralized Hodge conjecture.
610   $ageometric coniveau.
610   $ahyper-Khler manifolds.
610   $aintegral coefficients.
610   $aintegral cohomological decomposition.
610   $amixed Hodge structures.
610   $aprojective space.
610   $arational equivalence.
610   $asmall diagonal.
610   $asmooth projective varieties.
610   $aspreading principle.
610   $atorsion coefficients.
610   $atranscendental cohomology.
610   $aunramified cohomology.
610   $avariety.
615  0$aAlgebraic varieties.
615  0$aDecomposition (Mathematics).
615  0$aHomology theory.
615  0$aMathematics.
615  0$aAlgebraic varieties
615  0$aDecomposition (Mathematics)
615  0$aHomology theory
676   $a516.35
686   $aSI 830$2rvk
700   $aVoisin$b Claire$0350778
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910819930903321
996   $aChow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)$94012056
997   $aUNINA