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Stein spaces and Stein algebras

Olivier Benoist

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.

Stein spaces and Stein algebras

Abstract

We prove that the category of Stein spaces and holomorphic maps is anti-equivalent to the category of Stein algebras and -algebra morphisms. This removes a finite dimensionality hypothesis from a theorem of Forster.
Paper Structure (3 sections, 12 theorems, 6 equations)

This paper contains 3 sections, 12 theorems, 6 equations.

Table of Contents

  1. Tools from Oka theory
  2. Holomorphic maps with finite-dimensional fibers
  3. Morphisms of Stein algebras

Key Result

Theorem 1

The contravariant functor given by $S\mapsto \mathcal{O}(S)$ is an anti-equivalence of categories.

Theorems & Definitions (21)

  • Theorem 1: Theorem \ref{['th']}
  • Theorem 2: Theorem \ref{['prop']}
  • Proposition 1.1
  • Lemma 1.2
  • proof
  • Proposition 1.3
  • proof
  • Theorem 2.1
  • proof
  • Lemma 2.2
  • ...and 11 more