Unstable algebraic K-theory: homological stability and other observations

TL;DR

This paper studies the stability properties of reductive Borel-Serre categories, showing they have better homological stability than general linear groups and serve as explicit models for Yuan's partial algebraic K-theory.

Contribution

It introduces an improved stability analysis of reductive Borel-Serre categories and connects them to Yuan's partial algebraic K-theory, advancing understanding of unstable algebraic K-theory.

Findings

Reductive Borel-Serre categories exhibit superior homological stability.

They provide explicit models for Yuan's partial algebraic K-theory.

The work enhances the understanding of unstable algebraic K-theory.

Abstract

We investigate stability properties of the reductive Borel-Serre categories; these were introduced as a model for unstable algebraic K-theory in previous work. We see that they exhibit better homological stability properties than the general linear groups. We also show that they provide an explicit model for Yuan's partial algebraic K-theory.