Abstract
This paper studies universal families of stable genus-2 curves with level structure. Among other things, it is shown that the -part is spanned by divisor classes, and that there are no cycles of type in the third cohomology of the first direct image of under projection to the moduli space of curves. Using this, it shown that the Hodge and Tate conjectures hold for these varieties.
Citation
Donu Arapura. "Algebraic cycles on genus-2 modular fourfolds." Algebra Number Theory 13 (1) 211 - 225, 2019. https://doi.org/10.2140/ant.2019.13.211
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