2024/07/16 by Xander Faber, Faber, Xander
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2407.12089
openalex publication_date 2024/07/16 · openalex created_date 2024/10/25 · openalex updated_date 2026/07/28
Let K be a complete discretely valued field. An extension L/K is "weakly totally ramified" if the residue extension is purely inseparable. We sharpen a result of Ax by showing that any Galois-invariant disk in the algebraic closure of K contains an element that generates a separable weakly totally ramified extension. As an application, we prove that elliptic curves and dynamical systems on ℙ1 achieve semistable reduction over a separable weakly totally ramified extension of the base field. We also obtain several arithmetic consequences for torsion points on elliptic curves and preperiodic points for dynamical systems.