Nagata's compactification theorem for normal toric varieties over a valuation ring of rank one

Abstract

We prove, using invariant Zariski-Riemann spaces, that every normal toric variety over a valuation ring of rank one can be embedded as an open dense subset into a proper toric variety equivariantly. This extends a well known theorem of Sumihiro for toric varieties over a field to this more general setting.

arXiv comment1 figure, 14 pages. Few modifications after the comments of the referee. Accepted by the Michigan Mathematical Journal