Geodesic
Classification of normal toric varieties over a valuation ring of rank one
Documenta mathematica, Tome 20 (2015), pp. 171-198
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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.
DOI : 10.4171/dm/488
Classification : 13F30, 14L30, 14M25 
@article{10_4171_dm_488,
     author = {Alejandro Soto and Walter Gubler},
     title = {Classification of normal toric varieties over a valuation ring of rank one},
     journal = {Documenta mathematica},
     pages = {171--198},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/488},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/488/}
}
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Alejandro Soto; Walter Gubler. Classification of normal toric varieties over a valuation ring of rank one. Documenta mathematica, Tome 20 (2015), pp. 171-198. doi: 10.4171/dm/488

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