JournalsdmVol. 20pp. 171–198

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

  • Walter Gubler

    Fakultät für Mathematik Department of Mathematics Universität Regensburg KU Leuven Universitätsstrasse 31 Celestijnenlaan 200B D-93040 Regensburg B-3001 Heverlee

  • Alejandro Soto

    Fakultät für Mathematik Department of Mathematics Universität Regensburg KU Leuven Universitätsstrasse 31 Celestijnenlaan 200B D-93040 Regensburg B-3001 Heverlee
Classification of normal toric varieties over a valuation ring of rank one cover
Download PDF

This article is published open access.

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

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

DOI 10.4171/DM/488