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2009 | 7 | 4 | 606-616
Tytuł artykułu

Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves over perfect fields. For example, if k is finitely generated over ℚ and X → C is a quadric fibration of odd relative dimension at least 11, then CH i(X) is finitely generated for i ≤ 4.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
4
Strony
606-616
Opis fizyczny
Daty
wydano
2009-12-01
online
2009-10-31
Twórcy
Bibliografia
  • [1] Colliot-Thélène J.-L, Skorobogatov A., Groupe de Chow des zéro-cycles sur les fibrés en quadriques, K-Theory, 1993, 7, 477–500 http://dx.doi.org/10.1007/BF00961538[Crossref]
  • [2] Conrad B., Chows K/k-image and K/k-trace, and the Lang-Néron theorem, Enseign. Math. (2), 2006, 52, 37–108
  • [3] Fulton W., Intersection theory, Second Ed., Springer-Verlag, 1998
  • [4] González-Avilés C, Algebraic cycles on Severi-Brauer schemes of prime degree over a curve, Math. Res. Lett., 2008, 15(1), 51–56 [Crossref]
  • [5] Gros M., 0-cycles de degré zéro sur les surfaces fibrées en coniques, J. Reine Angew. Math., 1987, 373, 166–184
  • [6] Kahn B., Rost M., Sujatha R, Unramified cohomology of quadrics I, Amer. Math. J., 1998, 120(4), 841–891 http://dx.doi.org/10.1353/ajm.1998.0029[Crossref]
  • [7] Karpenko N., Algebro-geometric invariants of quadratic forms, Leningrad Math. J., 1991, 2(1), 119–138
  • [8] Karpenko N., Chow groups of quadrics and the stabilization conjecture, Adv. Soviet Math., 1991, 4, 3–8
  • [9] Karpenko N., Chow groups of quadrics and index reduction formulas, Nova J. Algebra Geom., 1995, 3(4), 357–379
  • [10] Karpenko N., Order of torsion in CH 4 of quadrics, Doc. Math., 1996, 1, 57–65
  • [11] Karpenko N., Merkurjev A., Chow groups of projective quadrics, Leningrad Math. J., 1991, 2(3), 655–671
  • [12] Karpenko N., Merkurjev A., Rost projectors and Steenrod operations, Doc. Math., 2002, 7, 481–493
  • [13] Lam T.Y., The algebraic theory of quadratic forms, W.A. Benjamin, Inc. Reading, Massachussettss, 1973
  • [14] Milne J.S., Arithmetic Duality Theorems, Perspectives in Mathematics, vol. 1, Academic Press Inc., Orlando 1986
  • [15] Parimala R., Suresh V., Zero-cycles on quadric fibrations: Finiteness theorems and the cycle map, Invent. Math., 1995, 122, 83–117 http://dx.doi.org/10.1007/BF01231440[Crossref]
  • [16] Rost M., Chow groups with coefficients, Doc. Math., 1996, 1, 319–393
  • [17] Sherman C., Some theorems on the K-Theory of coherent sheaves, Comm. Algebra, 1979, 7(14), 1489–1508 http://dx.doi.org/10.1080/00927877908822414[Crossref]
  • [18] Swan R., Zero-cycles on quadric hypersurfaces, Proc. Amer. Math. Soc., 1989, 107, 43–46 http://dx.doi.org/10.2307/2048032[Crossref]
  • [19] Weibel C., An introduction to homological algebra, Cambridge Stud. Adv. Math., Cambridge Univ. Press, 1994, 38
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0043-2
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