Motivic homology of semiabelian varieties

TL;DR

This paper extends classical results on Chow groups of abelian varieties to semiabelian varieties and motivic (co)homology, utilizing a decomposition of motives in Voevodsky's category.

Contribution

It introduces a generalization of Chow group results to semiabelian varieties and applies motivic homology techniques with a new motive decomposition.

Findings

Generalization of Chow group results to semiabelian varieties

Application of motive decomposition in Voevodsky's category

Advancement in motivic (co)homology understanding

Abstract

We generalize some classical results on Chow group of an abelian variety to semiabelian varieties and to motivic (co)homology, using a result of Ancona--Enright-Ward--Huber on a decomposition of the motive of a semiabelian variety in the Voevodsky's category.