Diophantine equations after Fermat’s last theorem

Samir Siksek[1]

  • [1] Mathematics Institute University of Warwick Coventry, CV4 7AL, United Kingdom

Journal de Théorie des Nombres de Bordeaux (2009)

  • Volume: 21, Issue: 2, page 423-434
  • ISSN: 1246-7405

Abstract

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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, ...?

How to cite

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Siksek, Samir. "Diophantine equations after Fermat’s last theorem." Journal de Théorie des Nombres de Bordeaux 21.2 (2009): 423-434. <http://eudml.org/doc/10889>.

@article{Siksek2009,
abstract = {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, ...?},
affiliation = {Mathematics Institute University of Warwick Coventry, CV4 7AL, United Kingdom},
author = {Siksek, Samir},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {exponential Diophantine equations; Wiles theory; Baker's theory},
language = {eng},
number = {2},
pages = {423-434},
publisher = {Université Bordeaux 1},
title = {Diophantine equations after Fermat’s last theorem},
url = {http://eudml.org/doc/10889},
volume = {21},
year = {2009},
}

TY - JOUR
AU - Siksek, Samir
TI - Diophantine equations after Fermat’s last theorem
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2009
PB - Université Bordeaux 1
VL - 21
IS - 2
SP - 423
EP - 434
AB - 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, ...?
LA - eng
KW - exponential Diophantine equations; Wiles theory; Baker's theory
UR - http://eudml.org/doc/10889
ER -

References

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  7. Y. Bugeaud, M. Mignotte and S. Siksek, Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell Equation. Compositio Mathematica 142 (2006), 31–62. Zbl1128.11013MR2196761
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