Algebraic cycles on genus two modular fourfolds

Abstract

We study universal families of stable genus two 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. Using this, we deduce the Hodge and Tate conjectures hold for these varieties.

This is in final form. To appear in Algebra and Number Theory

References in corpus (1)

• Cohomology of local systems on the moduli of principally polarized abelian surfaces

Cited by in corpus (1)

• Hodge cycles and the Leray filtration