Picard group of the forms of the affine line and of the additive group

2016/10/07 by Raphaël Achet, Achet, Raphaël
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Meromorphic and Entire Functions

paper · doi:10.48550/arxiv.1610.02240

openalex publication_date 2016/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain an explicit upper bound on the torsion of the Picard group of the forms of the affine line and their regular completions. We also obtain a sufficient condition for the Picard group of the forms of the affine line to be non trivial and we give examples of non trivial forms of the affine line with trivial Picard groups.

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