2021/01/27 by Nicole Looper, Looper, Nicole, Joseph H. Silverman +3 · 1 citation
Arts and Humanities · Mathematics · Social Sciences · #11G30 #11G50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT) #Vietnamese History and Culture Studies
paper · doi:10.48550/arxiv.2101.11593
openalex publication_date 2021/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that any smooth projective geometrically connected non-isotrivial curve of genus g≥ 2 over a one-dimensional function field of any characteristic has at most 16g2+32g+124 torsion points for any Abel-Jacobi embedding of the curve into its Jacobian. The proof uses Zhang's admissible pairing on curves, the arithmetic Hodge index theorem over function fields, and the metrized graph analogue of Elkies' lower bound for the Green function. More generally, we prove an explicit Bogomolov-type result bounding the number of geometric points of small Néron-Tate height on the curve embedded into its Jacobian.