Algebraic cycles on genus-2 modular fourfolds

Arapura, Donu

doi:10.2140/ant.2019.13.211

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Algebraic cycles on genus-2 modular fourfolds

Donu Arapura

Vol. 13 (2019), No. 1, 211–225

DOI: 10.2140/ant.2019.13.211

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.

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Keywords

Hodge conjecture, Tate conjecture, moduli of curves

Mathematical Subject Classification 2010

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

Vol. 13, No. 1, 2019