## Algebra & Number Theory

### Algebraic cycles on genus-2 modular fourfolds

Donu Arapura

#### Abstract

This paper studies universal families of stable genus-2 curves with level structure. Among other things, it is shown that the $(1,1)$-part is spanned by divisor classes, and that there are no cycles of type $(2,2)$ 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.

#### Article information

Source
Algebra Number Theory, Volume 13, Number 1 (2019), 211-225.

Dates
Revised: 11 November 2018
Accepted: 30 November 2018
First available in Project Euclid: 27 March 2019

https://projecteuclid.org/euclid.ant/1553652028

Digital Object Identifier
doi:10.2140/ant.2019.13.211

Mathematical Reviews number (MathSciNet)
MR3917918

Zentralblatt MATH identifier
07041709

Subjects
Primary: 14C25: Algebraic cycles

#### Citation

Arapura, Donu. Algebraic cycles on genus-2 modular fourfolds. Algebra Number Theory 13 (2019), no. 1, 211--225. doi:10.2140/ant.2019.13.211. https://projecteuclid.org/euclid.ant/1553652028

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