Hodge Structures Associated to SU(p, 1)

Abstract

Let A be an abelian variety over ℂ such that the semisimple part of the Hodge group of A is a product of copies of SU(p, 1) for some p > 1. We show that any effective Tate twist of a Hodge structure occurring in the cohomology of A is isomorphic to a Hodge structure in the cohomology of some abelian variety.

Key Words:

• Abelian variety
• Hodge structure
• Kuga fiber variety
• Tate twist

2010 Mathematics Subject Classification:

• 14C30
• 14K20

ACKNOWLEDGMENTS

I am grateful to the referees for detailed and insightful comments which have led to significant improvements to this paper.

Notes

Communicated by S. Kleiman.