Mathematical Research Letters

Volume 22 (2015)

Number 3

A realization for a $\mathbb{Q}$-Hermitian variation of Hodge structure of Calabi-Yau type with real multiplication

Pages: 967 – 982

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n3.a17

Author

Zheng Zhang (Department of Mathematics, Stony Brook University, Stony Brook, New York, U.S.A.)

Abstract

We show that the $\mathbb{Q}$-descents of the canonical $\mathbb{R}$-variation of Hodge structure of Calabi–Yau type over a tube domain of type $A$ can be realized as sub-variations of Hodge structure of certain $\mathbb{Q}$-variations of Hodge structure which are naturally associated to abelian varieties of (generalized) Weil type.

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Published 20 May 2015