Work

Torus actions on affine varieties over characteristic zero fields

Year: 2022

Type: preprint

Abstract: Using Galois descent tools, we extend the Altmann-Hausen presentation of normal affine algebraic varieties endowed with an effective torus action over an algebraically closed field of characteristic zero to the case where the ground field is an arbitrary field of characteristic zero. In this context, the acting torus may have non-trivial torsors and we need additional data to encode such varieties. Finally, we focus on affine varieties endowed with a two-dimensional torus action and we provide a method for determining when a torsor is trivial, in which case the Altmann-Hausen presentation simplifies.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2208.01495

Author: Gillard, Pierre-Alexandre

Institutions: Université de Bourgogne, Institut de Mathématiques de Bourgogne

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité

OpenAlex ID: W4289529737

Cites:

Cited by: 1

Related to: 10