Deligne's conjecture on 1-motives

被引：18
作者：
Barbieri-Viale, L
Rosenschon, A
Saito, M
机构：
[1] Univ Roma La Sapienza, Rome, Italy
[2] Duke Univ, Durham, NC 27706 USA
[3] Rims Kyoto Univ, Kyoto, Japan
来源：
ANNALS OF MATHEMATICS | 2003年 / 158卷 / 02期
关键词：
D O I：
10.4007/annals.2003.158.593
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We reformulate a conjecture of Deligne on 1-motives by using the integral weight filtration of Gillet and Soule on cohomology, and prove it. This implies the original conjecture up to isogeny. If the degree of cohomology is at most two, we can prove the conjecture for the Hodge realization without isogeny, and even for 1-motives with torsion.
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页码：593 / 633
页数：41
相关论文
共 34 条
  • [1] Barbieri-Viale L, 2002, ALGEBRAIC GEOMETRY -GERMANY, P25
  • [2] BARBIERIVIALE L, 2001, MEM SOC MATH FRANCE, V87
  • [3] Beilinson A., 1985, J SOVIET MATH, V30, P2036, DOI [10.1007/BF02105861, DOI 10.1007/BF02105861]
  • [4] Beilinson A. A., 1986, Applications of Algebraic K-theory to Algebraic Geometry and Number Theory, Part I, Proceedings of a Summer Research Conference held June 12-18, 1983, Boulder, Colorado, P35
  • [5] BEILINSON AA, 1982, ASTERISQUE, P7
  • [6] Biswas J, 2000, DUKE MATH J, V101, P427
  • [7] ALGEBRAIC CYCLES AND HIGHER K-THEORY
    BLOCH, S
    [J]. ADVANCES IN MATHEMATICS, 1986, 61 (03) : 267 - 304
  • [8] Carlson J. A., 1980, Journees de Geometrie Algebrique d'Angers, P107
  • [9] CARLSON JA, 1985, COMPOS MATH, V56, P271
  • [10] DELIGNE P, 1974, PUBLICATIONS MATH IH, V44, P5, DOI 10.1007/BF02685881
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