The generalized Fermat equation over totally real number fields

Doctoral thesis English OPEN
Deconinck, Heline
  • Subject: QA
    acm: ComputingMilieux_LEGALASPECTSOFCOMPUTING
  • References (10)

    Chapter 5 Generalizing over totally real elds: preliminaries 55 5.1 Eichler-Shimura . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.2 The Frey curve and its modularity . . . . . . . . . . . . . . . 57 5.3 Level lowering . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 1 (mod 4) 3 (mod 4): 1 (mod 4) 3 (mod 4):

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    [2] W. Bosma, J. Cannon and C. Playoust, The Magma Algebra System I: The User Language, J. Symb. Comp. 24 (1997), 235{265. (See also http://magma.maths.usyd.edu.au/magma/)

    [3] C. Breuil, B. Conrad, F. Diamond and R. Taylor, On the modularity of elliptic curves over Q: wild 3-adic exercises, J. Amer. Math. Soc. 14 No.4 (2001), 843{939.

    [4] P. Charollois, Generalized Fermat equations (d'apres Halberstadt-Kraus) Clay Mathematics Proceedings, Volume 8, 2009, 83{89.

    [18] E. Halberstadt and A. Kraus, Courbes de Fermat: resultats et problemes, J. reine angew. Math. 548 (2002), 167{234.

    [19] Y. Hellegouarch http://www.math.unicaen.fr/ nitaj/hellegouarch.html.

    [20] H. Hida, On abelian varieties with complex multiplication as factors of the Jacobians of Shimura curves, Amer. J. Math. 103 (1981), no. 4, 726{776.

    [37] N. P. Smart, The Algorithmic Resolution of Diophantine Equations, London Mathematical Society Student Texts 41, 1998.

    [39] R. L. Taylor and A. Wiles, Ring theoretic properties of certain Hecke algebras, Annals of Math. 141 (1995), 553{572.

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