Algebra & Number Theory

Algebraic cycles on genus-2 modular fourfolds

Donu Arapura

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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 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
Received: 28 February 2018
Revised: 11 November 2018
Accepted: 30 November 2018
First available in Project Euclid: 27 March 2019

Permanent link to this document
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

Keywords
Hodge conjecture Tate conjecture moduli of curves

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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