Hodge structures of CM-type

Details Hodge structures of CM-type Hodge structures of CM-type

2006-01-03

arxiv.org/abs/math/0601052v1

Journal of the Ramanujan Mathematical Society 20 (2005), 155-162

Mathematics

Algebraic Geometry

9 pages

Scientific paper

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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