Journal of the Ramanujan Mathematical Society

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Hodge Structures of CM-Type


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1 Department of Mathematics, East Carolina University, Greenville, NC 27858, United States
     

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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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  • Hodge Structures of CM-Type

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Authors

Salman Abdulali
Department of Mathematics, East Carolina University, Greenville, NC 27858, United States

Abstract


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.