Cox rings over nonclosed fields

Abstract

We give a definition of Cox rings and Cox sheaves for varieties over nonclosed fields that is compatible with torsors under quasitori, including universal torsors. We study their existence and classification, we make the relation to torsors precise, and we present arithmetic applications.

30 pages; reorganized, Section 5 shortened

References in corpus (5)

• ${\overline{M}}_{0,n}$ is not a Mori Dream Space
• A software package for Mori dream spaces
• Twisted forms of toric varieties
• Imaginary quadratic points on toric varieties via universal torsors
• Description de torseurs quasi-versels pour une famille de surfaces fibrées en coniques

Cited by in corpus (1)

• Integral points on singular del Pezzo surfaces