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2003 | 1 | 4 | 510-560
Tytuł artykułu

Variation of the reduction type of elliptic curves under small base change with wild ramification

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the variation of the reduction type of elliptic curves under base change. A complete description of the variation is given when the base field is the p-adic field and the base change is of small degree.
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
4
Strony
510-560
Opis fizyczny
Daty
wydano
2003-12-01
online
2003-12-01
Twórcy
Bibliografia
  • [1] Clemens Adelmann: The decomposition of primes in torsion point fields, Springer-Verlag, Berlin, 2001.
  • [2] Pilar Bayer and Anna Rio: “Dyadic exercises for octahedral extensions”, J. Reine Angew. Math., Vol. 517, (1999), pp. 1–17.
  • [3] J.E. Cremona: Algorithms for modular elliptic curves, Cambridge University Press, Cambridge, second edition, 1997.
  • [4] Marcus du Sautoy and Ivan Fesenko: “Where the wild things are: ramification groups and the Nottingham group”, In: New horizons in pro-p groups. Birkhäuser Boston, Boston, MA, 2000, pp. 287–328.
  • [5] Jean-Marc Fontaine: “Groupes de ramification et représentations d'Artin”, Ann. Sci. École Norm. Sup. (4), Vol. 4, (1971), pp. 337–392.
  • [6] Helmut Hasse: “Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage”, Math. Z., Vol. 31, (1930), pp. 565–582. http://dx.doi.org/10.1007/BF01246435
  • [7] Luise-Charlotte Kappe and Bette Warren: “An elementary test for the Galois group of a quartic polynomial”, Amer. Math. Monthly, Vol. 96, (1989), pp. 133–137. http://dx.doi.org/10.2307/2323198
  • [8] Masanari Kida: “Ramification in the division fields of an elliptic curve”, To appear in Abh. Math. Sem. Univ. Hamburg.
  • [9] Masanari Kida; “Computing elliptic curves using KASH”, In: Arjeh M. Cohen, Xiao-Shan Gao, Nobuki Takayama, (Eds): Mathematical Software, World Scientific, 2002, pp. 250–260.
  • [10] Alain Kraus: “Sur le défaut de semi-stabilité des courbes elliptiques à réduction additive”, Manuscripta Math., Vol. 69, (1990), pp. 353–385.
  • [11] Pascual Llorente and Enric Nart: “Effective determination of the decomposition of the rational primes in a cubic field”, Proc. Amer. Math. Soc., Vol. 87, 1983, pp. 579–585. http://dx.doi.org/10.2307/2043339
  • [12] Paul Lockhart, Michael Rosen, Joseph H. Silverman: “An upper bound for the conductor of an abelian variety”, J. Algebraic Geom., Vol. 2(1993), pp. 569–601.
  • [13] E. Maus: “Arithmetisch disjunkte Körper”, J. Reine Angew. Math., Vol. 226, (1967), pp. 184–203.
  • [14] Hirotada Naito: “Dihedral extensions of degree 8 over the rational p-adic fields”, Proc. Japan Acad. Ser. A Math. Sci., Vol. 71(1995), pp. 17–18. http://dx.doi.org/10.3792/pjaa.71.17
  • [15] Hirotada Naito: “Local fields generated by trisection points of elliptic curves”, Sūrikaisekikenkyūsho Kōkyūroku, Vol. 971, (1996), pp. 153–159, Algebraic number theory and Fermat's problem (Japanese), Kyoto, 1995.
  • [16] Hirotada Naito: “Local fields generated by 3-division points of elliptic curves”, Proc. Japan Acad. Ser. A Math. Sci., Vol. 78, (2002), pp. 173–178.
  • [17] Jürgen Neukirch: Algebraische Zahlentheorie, Springer-Verlag, Berlin, 1992.
  • [18] Ioannis Papadopoulos: “Sur la classification de Néron des courbes elliptiques en caractéristique résiduelle 2 et 3”, J. Number Theory, Vol. 44, (1993), pp. 119–152. http://dx.doi.org/10.1006/jnth.1993.1040
  • [19] Sebastian Pauli: “Factoring polynomials over local fields”, J. Symbolic Comput., Vol. 32, (2001), pp. 533–547. http://dx.doi.org/10.1006/jsco.2001.0493
  • [20] Sebastian Pauli and Xavier-François Roblot: “On the computation of all extensions of a p-adic field of a given degree”, Math. Comp., Vol. 70, (2001), pp. 1641–1659 (electronic). http://dx.doi.org/10.1090/S0025-5718-01-01306-0
  • [21] Jean-Pierre Serre: Corps locaux. Hermann, Paris, 1968. Deuxième édition, Publications de l'Université de Nancago, No. VIII.
  • [22] Jean-Pierre Serre: “Propriétés galoisiennes des points d'ordre fini des courbes elliptiques”, Invent. Math., Vol. 15, (1972), pp. 259–331. http://dx.doi.org/10.1007/BF01405086
  • [23] Jean-Pierre Serre and John Tate: “Good reduction of abelian varieties”, Ann. of Math. (2), Vol. 88, (1968), pp. 492–517. http://dx.doi.org/10.2307/1970722
  • [24] Joseph H. Silverman: The arithmetic of elliptic curves, Springer-Verlag, New York, 1986.
  • [25] Joseph H. Silverman: Advanced topics in the arithmetic of elliptic curves, Springer-Verlag, New York, 1994.
  • [26] André Weil: “Exercices dyadiques”, Invent. Math., Vol. 27, (1974), pp. 1–22. http://dx.doi.org/10.1007/BF01389962
  • [27] Masakazu Yamagishi: “On the number of Galois p-extensions of a local field”, Proc. Amer. Math. Soc., Vol. 123, (1995), pp. 2373–2380. http://dx.doi.org/10.2307/2161262
  • [28] Sunao Yamamoto: “On a property of the Hasse's function in the ramification theory”, Mem. Fac. Sci. Kyushu Univ. Ser. A, Vol. 22, (1968), pp. 96–109.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475181
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