Diophantine equations after Fermat’s last theorem
Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 2, p. 423-434

These are expository notes that accompany my talk at the 25th Journées Arithmétiques, July 2–6, 2007, Edinburgh, Scotland. I aim to shed light on the following two questions:

  • (i) Given a Diophantine equation, what information can be obtained by following the strategy of Wiles’ proof of Fermat’s Last Theorem?
  • (ii) Is it useful to combine this approach with traditional approaches to Diophantine equations: Diophantine approximation, arithmetic geometry, ...?

Cet article reprend les notes de mon exposé aux 25-ièmes Journées Arithmétiques, du 2 au 6 juillet 2007 à Edimbourg en Écosse. J’ai pour but d’apporter un peu de lumière sur les deux questions suivantes :

  • (i) Étant donnée une équation diophantienne, quelle information peut-on obtenir en suivant la stratégie de Wiles pour sa preuve du théorème de Fermat ?
  • (ii) Est-il utile de combiner cette approche avec les approches traditionnelles des équations diophantiennes : approximation diophantienne, géométrie arithmétique, ... ?
@article{JTNB_2009__21_2_423_0,
     author = {Siksek, Samir},
     title = {Diophantine equations after Fermat's last theorem},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {2},
     year = {2009},
     pages = {423-434},
     doi = {10.5802/jtnb.679},
     mrnumber = {2541434},
     zbl = {pre05620659},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2009__21_2_423_0}
}
Siksek, Samir. Diophantine equations after Fermat’s last theorem. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 2, pp. 423-434. doi : 10.5802/jtnb.679. http://www.numdam.org/item/JTNB_2009__21_2_423_0/

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