Abstract
There are infinitely many fundamentally distinct families of polarized Abelian fourfolds of Weil type with multiplication from the cyclotomic field of cube roots of unity. The Hodge conjecture is shown to hold at a sufficiently general fiber in any of these families.
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Schoen, C. Addendum to: Hodge Classes on Self-Products of a Variety with an Automorphism. Compositio Mathematica 114, 321–328 (1998). https://doi.org/10.1023/A:1000566205021
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DOI: https://doi.org/10.1023/A:1000566205021