Somekawa's K-groups and Voevodsky's Hom groups (preliminary version)

TL;DR

This paper constructs a surjective homomorphism linking Somekawa's K-groups of semi-abelian varieties to Voevodsky's Hom groups, advancing the understanding of their relationship within motivic homotopy theory.

Contribution

It introduces a surjective homomorphism from Somekawa's K-group to Voevodsky's Hom group, establishing a new connection in motivic cohomology.

Findings

Established a surjective homomorphism between the two groups

Connected algebraic K-theory with motivic homotopy theory

Provided a new tool for studying semi-abelian varieties in motives

Abstract

We construct a surjective homomorphism from Somekawa's K-group associated to a finite collection of semi-abelian varieties over a perfect field to a corresponding Hom group in Voevodsky's triangulated category of effective motivic complexes.