The equivalence of Friedlander-Mazur and standard conjectures for threefolds

TL;DR

This paper proves that for three-dimensional complex smooth projective varieties, the Friedlander-Mazur conjecture and the standard conjectures are equivalent, leading to new examples where these conjectures hold.

Contribution

It establishes the equivalence of Friedlander-Mazur and standard conjectures for threefolds, providing new cases where these conjectures are verified.

Findings

Friedlander-Mazur conjecture implies standard conjectures for threefolds

The two conjectures are equivalent in dimension three

New examples of varieties satisfying the standard conjectures

Abstract

We show that the Friedlander-Mazur conjecture holds for a complex smooth projective variety X of dimension three implies the standard conjectures hold for X. This together with a result of Friedlander yields the equivalence of the two conjectures in dimension three. From this we provide some new examples whose standard conjectures hold.