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

  Published:2004-08-01
 Printed: Aug 2004
  • Élie Cali
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Abstract

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 $L/K_{nr}$.
MSC Classifications: 11G07 show english descriptions Elliptic curves over local fields [See also 14G20, 14H52] 11G07 - Elliptic curves over local fields [See also 14G20, 14H52]
 

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