Classification of Normal Toric Varieties over a Valuation Ring of Rank One
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.
2010 Mathematics Subject Classification: 14M25, 14L30, 13F30
Keywords and Phrases:
Full text: dvi.gz 65 k, dvi 213 k, ps.gz 350 k, pdf 333 k.
Home Page of DOCUMENTA MATHEMATICA