Tate twists of Hodge structures arising from abelian varieties of type IV

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

10.1016/j.jpaa.2011.10.005

We show that certain abelian varieties A have the property that for every
Hodge structure V in the cohomology of A, every effective Tate twist of V
occurs in the cohomology of some abelian variety. We deduce the general Hodge
conjecture for certain non-simple abelian varieties of type IV.

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