On the Bass Stable Rank of Stein Algebras

TL;DR

This paper calculates the Bass stable rank of Stein algebras of global sections on Stein spaces and applies this to factorization problems of invertible holomorphic matrices.

Contribution

It provides the first explicit computation of the Bass stable rank for Stein algebras and uses this to address matrix factorization issues.

Findings

Bass stable rank of Stein algebras is explicitly computed.

Results facilitate the factorization of invertible holomorphic matrices.

Application to complex geometry and algebraic K-theory.

Abstract

We compute the Bass stable rank of the ring $\Gamma(X,\mathcal O_X)$ of global sections of the structure sheaf $\mathcal O_X$ on a finite-dimensional Stein space $(X,\mathcal O_X)$ and then apply this result to the problem of the factorization of invertible holomorphic matrices on $X$.