2020/07/09 by Marco Maculan, Maculan, Marco
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2007.04659
openalex publication_date 2020/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be a complete non-trivially valued non-Archimedean field. Given an algebraic group over K on which every regular function is constant, any rigid analytic function is shown to be constant too. It follows that an algebraic group over K is affine if and only if the associated K-analytic space is Stein; that is, rigid analytic embeddings of it in an affine space may always be chosen to be given by algebraic functions. Arguably curiously, the corresponding statement over the complex numbers is false.