Algebra & Number Theory

Algebraic cycles on genus-2 modular fourfolds

Donu Arapura

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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

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14C25: Algebraic cycles

Hodge conjecture Tate conjecture moduli of curves


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.

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