#### Vol. 13, No. 1, 2019

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Algebraic cycles on genus-2 modular fourfolds

### Donu Arapura

Vol. 13 (2019), No. 1, 211–225
##### Abstract

This paper studies universal families of stable genus-2 curves with level structure. Among other things, it is shown that the $\left(1,1\right)$-part is spanned by divisor classes, and that there are no cycles of type $\left(2,2\right)$ in the third cohomology of the first direct image of $ℂ$ under projection to the moduli space of curves. Using this, it shown that the Hodge and Tate conjectures hold for these varieties.

##### Keywords
Hodge conjecture, Tate conjecture, moduli of curves
Primary: 14C25
##### Milestones
Received: 28 February 2018
Revised: 11 November 2018
Accepted: 30 November 2018
Published: 13 February 2019
##### Authors
 Donu Arapura Department of Mathematics Purdue University West Lafayette, IN United States