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Hodge structures of CM-type

Salman Abdulali
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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.

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Salman Abdulali. 2006-01-03. Hodge structures of CM-type. https://arxiv.org/abs/math/0601052

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