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arXiv · 1207.0569

Congruences of models of elliptic curves

Qing Liu·Huajun Lu
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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).

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Qing Liu, Huajun Lu. 2012-07-03. Congruences of models of elliptic curves. https://doi.org/10.1112/jlms%2Fjdt049

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