Lines crossing a tetrahedron and the Bloch group

TL;DR

This paper introduces a modified version of a Chow group using linear subvarieties, demonstrating its surjective relation to the Bloch group over any infinite field and describing its kernel.

Contribution

It presents a new linear-subvariety-based Chow group that maps onto the Bloch group, expanding understanding of algebraic K-theory and motivic cohomology.

Findings

Modified Chow group maps surjectively to Bloch group

Kernel of the map explicitly described

Applicable to any infinite field

Abstract

We consider a simple modification of the Chow group CH^2(Spec(k),3) using only linear subvarieties in affine spaces and show that it maps surjectively to the Bloch group B(k) for any infinite field k. We also describe the kernel of this map.