Affine vs. Stein in rigid geometry

Abstract

We investigate the relationship between affine and Stein varieties in the context of rigid geometry. We show that the two concepts are much more closely related than in complex geometry, e.g. they are equivalent for surfaces. This rests on the density of algebraic functions in analytic functions. One key ingredient to prove such a density statement is an extension result for Cartier divisors.

Several changes after revision. Final version, to appear in Compositio Math