Congruences of models of elliptic curves

Qing Liu (1) , Huajun Lu (2, 3)

1 Équipe Théorie des Nombres
2 IMB - Institut de Mathématiques de Bordeaux
3 MCM - Morningside Center of Mathematics

Let O_K be discrete valuation ring with a field of fractions K and a 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).

Domaines: Géométrie algébrique [math.AG]

Qing Liu, Huajun Lu. Congruences of models of elliptic curves. J. London Math. Soc., 2013, 88, pp.899-924. ⟨10.1112/jlms/jdt049⟩. ⟨hal-01023457⟩