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

Alejandro Soto

Published 2016-08-09Version 1

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 normal toric variety equivariantly. This extends a well known theorem of Sumihiro for toric varieties over a field to this more general setting.