JournalsdmVol. 20pp. 171–198

Classification of normal toric varieties over a valuation ring of rank one

  • Alejandro Soto

    Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Heverlee, Belgium

  • Walter Gubler

    Fakultät für Mathematik, Universität Regensburg, Universitätsstrasse 31, 93040 Regensburg, Germany
Classification of normal toric varieties over a valuation ring of rank one cover
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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.

Cite this article

Alejandro Soto, Walter Gubler, Classification of normal toric varieties over a valuation ring of rank one. Doc. Math. 20 (2015), pp. 171–198

DOI 10.4171/DM/488