Qing Liu, Huajun Lu
Published 2012-07-03, updated 2013-07-02Version 3
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).
Comments: Minor changes.To appear in J. London Math. Soc
Journal: J. London Math. Soc, 88 (2013), 899-924
Points of Low Height on Elliptic Curves and Surfaces, I: Elliptic surfaces over P^1 with small d
One-point covers of elliptic curves and good reduction
Abelian varieties isogenous to a power of an elliptic curve over a Galois extension
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