Défaut de semi-stabilité des courbes elliptiques dans le cas non ramifié

http://dx.doi.org/10.4153/CJM-2004-031-6
Canad. J. Math. 56(2004), 673-698

  Published:2004-08-01
 Printed: Aug 2004

Let $\overline {\Q_2}$ be an algebraic closure of $\Q_2$ and $K$ be an unramified finite extension of $\Q_2$ included in $\overline {\Q_2}$. Let $E$ be an elliptic curve defined over $K$ with additive reduction over $K$, and having an integral modular invariant. Let us denote by $K_{nr}$ the maximal unramified extension of $K$ contained in $\overline {\Q_2}$. There exists a smallest finite extension $L$ of $K_{nr}$ over which $E$ has good reduction. We determine in this paper the degree of the extension $L/K_{nr}$.