Congruences of models of elliptic curves
Algebraic Geometry
2023-12-06 v3 Number Theory
Abstract
Let O_K be a discrete valuation ring with field of fractions K and perfect residue field. Let E be an elliptic curve over K, let L/K be a finite Galois extension and let O_L be the integral closure of O_K in L. Denote by X' the minimal regular model of E_L over O_L. We show that the special fibers of the minimal Weierstrass model and the minimal regular model of E over O_K are determined by the infinitesimal fiber X'_m together with the action of Gal(L/K), when m is big enough (depending on the minimal discriminant of E and the different of L/K).
Keywords
Cite
@article{arxiv.1207.0569,
title = {Congruences of models of elliptic curves},
author = {Qing Liu and Huajun Lu},
journal= {arXiv preprint arXiv:1207.0569},
year = {2023}
}
Comments
Minor changes. To appear in J. London Math. Soc