Stein spaces and Stein algebras

TL;DR

This paper establishes a duality between Stein spaces and Stein algebras, removing a finite dimensionality assumption from a key theorem, thus deepening the understanding of their categorical relationship.

Contribution

It proves the anti-equivalence between Stein spaces and Stein algebras without requiring finite dimensionality, extending Forster's theorem.

Findings

Category of Stein spaces is anti-equivalent to Stein algebras

Finite dimensionality hypothesis removed from Forster's theorem

Enhanced understanding of the duality between geometric and algebraic structures

Abstract

We prove that the category of Stein spaces and holomorphic maps is anti-equivalent to the category of Stein algebras and $\mathbb{C}$-algebra morphisms. This removes a finite dimensionality hypothesis from a theorem of Forster.