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{\textquoteright}s} last theorem}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {423--434}, publisher = {Universit\'e Bordeaux 1}, volume = {21}, number = {2}, year = {2009}, doi = {10.5802/jtnb.679}, mrnumber = {2541434}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.679/} }
TY - JOUR AU - Siksek, Samir TI - Diophantine equations after Fermat’s last theorem JO - Journal de théorie des nombres de Bordeaux PY - 2009 SP - 423 EP - 434 VL - 21 IS - 2 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.679/ DO - 10.5802/jtnb.679 LA - en ID - JTNB_2009__21_2_423_0 ER -
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://archive.numdam.org/articles/10.5802/jtnb.679/
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