Classification of normal toric varieties over a valuation ring of rank one
arXiv:1303.1987
Abstract
Normal toric varieties over a field or a discrete valuation ring are classified by rational polyhedral fans. We generalize this classification to normal toric varieties over an arbitrary valuation ring of rank one. The proof is based on a generalization of Sumihiro's theorem to this non-noetherian setting. These toric varieties play an important role for tropicalizations.
22 pages. Minor modifications after the comments of the referee. Accepted by Documenta Mathematica