Salman Abdulali
Abstract
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We show that any effective Hodge structure of CM-type occurs (without having to take a Tate twist) in the cohomology of some CM abelian variety over C. As a consequence we get a simple proof of the theorem (due to Hazama) that the usual Hodge conjecture for the class of all CM abelian varieties implies the general Hodge conjecture for the same class.
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We show that any effective Hodge structure of CM-type occurs (without having to take a Tate twist) in the cohomology of some CM abelian variety over C. As a consequence we get a simple proof of the theorem (due to Hazama) that the usual Hodge conjecture for the class of all CM abelian varieties implies the general Hodge conjecture for the same class.
Key concepts: Hodge conjecture, Mathematics, Hodge theory, Abelian group, Pure mathematics, Cohomology, Hodge structure, Conjecture