Algebra & Number Theory
- Algebra Number Theory
- Volume 13, Number 1 (2019), 211-225.
Algebraic cycles on genus-2 modular fourfolds
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.
Algebra Number Theory, Volume 13, Number 1 (2019), 211-225.
Received: 28 February 2018
Revised: 11 November 2018
Accepted: 30 November 2018
First available in Project Euclid: 27 March 2019
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14C25: Algebraic cycles
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