Electronic Resource
Springer
Compositio mathematica
117 (1999), S. 47-81
ISSN:
1570-5846
Keywords:
Abelian varieties
;
Tate conjecture
;
motives.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A Lefschetz class on a smooth projective variety is an element of the Q-algebra generated by divisor classes. We show that it is possible to define Q-linear Tannakian categories of abelian motives using the Lefschetz classes as correspondences, and we compute the fundamental groups of the categories. As an application, we prove that the Hodge conjecture for complex abelian varieties of CM-type implies the Tate conjecture for all Abelian varieties over finite fields, thereby reducing the latter to a problem in complex analysis.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1000776613765
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