Divisorial fans and algebraic torus actions over arbitrary fields

TL;DR

This paper offers a combinatorial algebro-geometric framework for describing normal algebraic varieties with torus actions over arbitrary fields, extending the classification of T-varieties.

Contribution

It introduces divisorial fans with Galois semilinear actions to characterize T-varieties over any field, completing the classification over arbitrary fields.

Findings

Provides a combinatorial description of T-varieties over arbitrary fields

Extends the classification of normal T-varieties to all fields

Uses divisorial fans with Galois actions for the description

Abstract

We provide a algebro-geometric combinatorial description of geometrically integral geometrically normal varieties endowed with an effective action of an algebraic torus over arbitrary fields. This description is achieved in terms of divisorial fans endowed with a Galois semilinear action. This work concludes the description of normal $T$-varieties over fields.