Hostname: page-component-7c8c6479df-94d59 Total loading time: 0 Render date: 2024-03-29T06:19:30.615Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  20 November 2018

Elie Cali*
Affiliation:
App. 231, 9 rue de Sèvres, 92100 Boulogne, France e-mail: elie.cali@wanadoo.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let $\overline{{{\mathbb{Q}}_{2}}}$ be an algebraic closure of ${{\mathbb{Q}}_{2}}$ and $K$ be an unramified finite extension of ${{\mathbb{Q}}_{2}}$ included in $\overline{{{\mathbb{Q}}_{2}}}$. 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 $\overline{{{\mathbb{Q}}_{2}}}$. 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 $L/{{K}_{nr}}$.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2004

References

Références

[1] Cali, É. et Kraus, A., Sur la p-différente du corps des points de -torsion des courbes elliptiques, ℓ ≠ p. Acta Arith. 104(2002), 121.Google Scholar
[2] Kraus, A., Sur le défaut de semi-stabilité des courbes elliptiques à réduction additive. Manuscripta Math. 69(1990), 353385.Google Scholar
[3] Papadopoulos, I., Sur la classification de Néron des courbes elliptiques en caractéristique résiduelle 2 et 3 . J. Number Theory 44(1993), 119152.Google Scholar
[4] Serre, J.-P. et Tate, J., Good reduction of abelian varieties. Ann. of Math. 88(1968), 492517.Google Scholar
[5] Tate, J., Algorithm for determining the type of singular fiber in an elliptic pencil, dans Modular Functions of One Variable IV. Lect. Notes in Math. 476, Springer-Verlag 1975.Google Scholar