Homology of $GL_3$ of function rings of elliptic curves

TL;DR

This paper describes the homology of the group $GL_3$ over function rings of affine elliptic curves, extending previous work on $GL_2$ and exploring potential applications to elliptic curve K-theory.

Contribution

It generalizes the understanding of homology from $GL_2$ to $GL_3$ over elliptic curve function rings, providing new insights for algebraic K-theory.

Findings

Homology of $GL_3$ over elliptic curve function rings characterized.

Connections to K-theory of elliptic curves discussed.

Extension of previous $GL_2$ results to $GL_3$.

Abstract

The note provides a description of the homology of $GL_3$ over function rings of affine elliptic curves over arbitrary fields, following the earlier work of Takahashi and Knudson in the case $GL_2$. Some prospects for applications to K-theory of elliptic curves are also discussed.