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Hodge classes on self-products of a variety with an automorphism. (English) Zbl 0663.14006
The author studies the Hodge conjecture for a special family of abelian varieties. He constructs first a Hodge structure on self-products of curves with an automorphism, then he constructs algebraic cycles the cohomology classes of which generate this Hodge structure.
He applies his results to prove the Hodge conjecture in the case of the Weil Hodge structure on abelian 4-folds with complex multiplication from the cyclotomic field of cubic roots of unity.
Reviewer: A.Papantonopoulou

MSC:
 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) 14J35 $$4$$-folds 14K05 Algebraic theory of abelian varieties
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References:
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