Affine vs. Stein in rigid geometry
Algebraic Geometry
2025-04-28 v2 Complex Variables
Number Theory
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.
Keywords
Cite
@article{arxiv.2305.08974,
title = {Affine vs. Stein in rigid geometry},
author = {Marco Maculan and Jérôme Poineau},
journal= {arXiv preprint arXiv:2305.08974},
year = {2025}
}
Comments
Several changes after revision. Final version, to appear in Compositio Math