Algebraic cycles on fiber bundles of Leray-Hirsch type

TL;DR

This paper establishes a Leray-Hirsch type theorem for Chow groups and applies it to investigate major conjectures in algebraic geometry, including the Hodge and Grothendieck's standard conjectures, for specific fiber bundles.

Contribution

It introduces a new theorem of Leray-Hirsch type for Chow groups and explores its implications for key conjectures in algebraic geometry.

Findings

Leray-Hirsch type theorem for Chow groups established

Applications to Hodge and Grothendieck's standard conjectures

Discussion on the Hodge conjecture for product varieties

Abstract

We give a theorem of Leray-Hirsch type for Chow groups and use it to study the Hogde and Grothendieck's standard conjectures for algebraic fiber bundles of Leray-Hirsch type. Morevoer, the Hodge conjecture for product varieties will also be considered.