Abstract
Let K be a field of characteristics 0 complete with respect to a discrete valuation v, with a perfect residue field of characteristic p>0. Let\(\vec K\) be an algebraic closure of K and Knr its maximal unramified subextension. Let E be an elliptic curve over K with an integral modular invariant. The curve E has potentially good reduction at v, and there exists a smallest extension L of Knr over which E has good reduction at v. The Galois group, Gal (L/Knr) is known in the case p≥5. In this paper we give receipts to determine this group in the cases p=2 and p=3.
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KRAUS, A.: Quelques remarques à propos des invariants, c4, c6 et Δ d'une courbe elliptique. Acta Arith.54, 76–80 (1989).
OGG, A.: Elliptic curves and wild ramification. Amer. J. of Math.89, 1–21 (1967).
SERRE, J.-P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Invent. Math.15, 259–331 (1972)
SERRE, J.-P. ET TATE, J.: Good reduction of abelian varieties. Ann. of Math.88, 492–517 (1968)
SILVERMAN, J.: The Arithmetic of Elliptic Curves. G.T.M.106, Springer-Verlag 1986
TATE, J.: Algorithm for determining the type of singular fiber in an elliptic pencil. Modular Functions of One Variable IV, Lect. Notes in Math.476, Springer-Verlag 1975
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Kraus, A. Sur le défaut de semi-stabilité des courbes elliptiques à réduction additive. Manuscripta Math 69, 353–385 (1990). https://doi.org/10.1007/BF02567933
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DOI: https://doi.org/10.1007/BF02567933