### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 116, 18 pages      arXiv:1503.08355      https://doi.org/10.3842/SIGMA.2018.116
Contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui

### Normal Functions over Locally Symmetric Varieties

Ryan Keast a and Matt Kerr b
a) Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
b) Department of Mathematics and Statistics, Washington University in St. Louis, St. Louis, MO 63130, USA

Received May 09, 2018, in final form October 22, 2018; Published online October 26, 2018

Abstract
We classify the irreducible Hermitian real variations of Hodge structure admitting an infinitesimal normal function, and draw conclusions for cycle-class maps on families of abelian varieties with a given Mumford-Tate group.

Key words: normal function; Hermitian symmetric domain; Mumford-Tate group; variation of Hodge structure; algebraic cycle.

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