On the Grassmannian homology of $\mathbbm{F}_2$ and $\mathbbm{F}_3$

TL;DR

This paper proves the vanishing of certain Grassmannian homology subgroups in the higher Chow groups over finite fields _2 and _3, using computational methods to establish new results in algebraic K-theory.

Contribution

It demonstrates the vanishing of specific Grassmannian homology subgroups in higher Chow groups over _2 and _3, providing new computational evidence in algebraic K-theory.

Findings

Vanishing of certain Grassmannian homology subgroups over _2 and _3

Use of computer calculations to verify algebraic K-theory conjectures

New results on Bloch's higher Chow groups in finite fields

Abstract

We prove the vanishing of the subgroup of Bloch's cubical higher Chow groups $CH^2(\text{Spec}(\MF_p),3)$, $p=2,3$, generated by the images of corresponding projective Grassmannian homology groups ${}^PGH_1^2(\MF_p)$ using computer calculations.