Abelian Varieties over Real Closed Fields

2023/05/30 by Nathanial Lowry, Lowry, Nathanial
Mathematics · #11G10 (Primary) #12J15 (Secondary) #14G27 #14K05 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2305.19246

openalex publication_date 2023/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we classify the possible group structures on the set of R-valued points of an abelian variety, where R is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over all abelian varieties of a fixed dimension and degree of polarization in a first-order fashion.

Related

• Real structures on ordinary Abelian varieties
• Polarizations on abelian varieties
• Abelian varieties over finite fields as basic abelian varieties
• Angehrn-Siu-Helmke's method applied to abelian varieties
• Moduli space of real abelian varieties with level structure