Homotopy invariance of higher K-theory for abelian categories

TL;DR

This paper proves that the K-theory of a noetherian abelian category remains unchanged under polynomial extension, generalizing the A^1-homotopy invariance known for noetherian schemes.

Contribution

It establishes the homotopy invariance of higher K-theory for noetherian abelian categories via base change functors, extending known results from schemes to categories.

Findings

Base change functor induces isomorphism on K-theory

Homotopy invariance applies to noetherian abelian categories

Generalizes A^1-homotopy invariance to categorical setting

Abstract

The main theorem in this paper is that the base change functor from a noetherian abelian category to its noetherian polynomial category induces an isomorphism on K-theory. The main theorem implies the well-known fact that A^1-homotopy invariance of K'-theory for noetherian schemes.