On inertial types of elliptic curves

2025/12/04 by Jose Castro-Moreno, Florit, Enric, Castro-Moreno, Jose +2
Mathematics · #11G07 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2512.05023

openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/08/01

Abstract

We classify the inertial Weil-Deligne types arising from elliptic curves over all finite extensions F/\mathbb Q_p. Based on this classification, we give a fully explicit description of the types and implement an algorithm that computes all inertial types of elliptic curves defined over a given F. As an application, we determine all inertial types arising from elliptic curves over any extension F/\mathbb Q_p of degree at most 3.

Citations

• On the generalized Fermat equation of signature (5,p,3)
• Families of p-adic fields
• Wild Galois representations: elliptic curves with wild cyclic reduction
• On Galois inertial types of elliptic curves over ℚ_ℓ
• Wild Galois representations: elliptic curves over a 2-adic field with non-abelian inertia action

Related

• On Galois inertial types of elliptic curves over ℚ_ℓ
• La constante de Manin et le degré modulaire d'une courbe elliptique
• Elliptic curves over ℚ_∞ are modular
• Generators for the elliptic curve E_(p,q) : y² = x³ - p²x + q²
• Local torsion primes and the class numbers associated to an elliptic curve over ℚ