Topological and Geometric filtration for products

TL;DR

This paper proves the Friedlander-Mazur conjecture for products of elliptic curves with certain threefolds and demonstrates its stability under surjective maps, with applications to uniruled and unirational varieties.

Contribution

It establishes the conjecture for specific product varieties and shows its stability under surjective maps, expanding its verified cases.

Findings

Friedlander-Mazur conjecture holds for elliptic curve products with certain threefolds.

The conjecture is stable under surjective morphisms.

Holds for uniruled threefolds and unirational varieties within certain ranges.

Abstract

We show that the Friedlander-Mazur conjecture holds for the product of an elliptic curve with some smooth projective variety of dimension 3. Moreover, we show that the Friedlander-Mazur conjecture is stable under a surjective map. As applications, we show that the Friedlander-Mazur conjecture holds uniruled threefolds and unirational varieties up to certain range.