Beilinson-Hodge cycles on semiabelian varieties

TL;DR

This paper proves Beilinson's conjecture for semiabelian varieties and products of curves by analyzing invariants under the Mumford-Tate group, confirming that rational cycles of a certain type originate from motivic cohomology.

Contribution

It establishes the conjecture for semiabelian varieties and products of curves using Mumford-Tate group invariants, extending previous results.

Findings

Beilinson's conjecture holds for semiabelian varieties.

Rational cycles of type (q,q) are from motivic cohomology in these cases.

The proof utilizes invariants under the Mumford-Tate group.

Abstract

Beilinson conjectured that all rational cycles of type (q,q) on the qth cohomology of a smooth complex algebraic variety should come from motivic cohomology. The purpose of this note is to prove this when the variety is a semiabelian variety or a product of curves. The proof is based on the study of invariants under the Mumford-Tate group.