The $K$-Theory of Finitely Many Commuting Endomorphisms

TL;DR

This paper computes the algebraic K-theory of a specific category of finite-dimensional modules over polynomial rings with multiple commuting variables, extending previous foundational work in the field.

Contribution

It generalizes Kelley and Spanier's results by calculating the K-theory for modules over multivariable polynomial rings, broadening understanding of algebraic K-theory in this context.

Findings

Explicit computation of K-theory for modules over k[t_1,...,t_n]

Extension of previous results to multiple variables

Provides new tools for algebraic K-theory of polynomial rings

Abstract

For a field $k$ we compute the $K$-theory of the exact category of $k[t_1,\dots,t_n]$-modules that are finite-dimensional over $k$, generalising the work of Kelley and Spanier.