Chabauty methods and covering techniques applied to generalized Fermat equations
Nils Bruin · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2002
The text before you is an adaptation of my doctoral thesis Chabauty methods and covering techniques applied to generalised Fermat equations, which I defended October 6, 1999 in Leiden.Subsequently, the thesis was awarded a prize of the Stieltjes Research School.As a result, I was offered the opportunity to have the text published as a CWI tract.I am very happy to get the chance to publish this work in its entirety.In this way, it retains a coherence that is lost if a text is chopped up in articles.I hope readers agree with me and will get as much joy out of reading as I got from writing it.Also, publishing this work as a CWI-tract instead of as a thesis at the Universiteit Leiden gives me a chance to thank people that helped me in writing it.First of all, I would like to thank my advisors Rob Tijdeman and Frits Beukers for the guidance, support and freedom they offered me during the four years I worked on this subject.Their comments and suggestions helped me very much in my research and my writing.Special thanks also goes to Ed Schaefer who visited Leiden during spring 1999.First he accepted the function of referee and then exceeded his obligations and even took on the first correction of some parts of the manuscript.His enthusiasm and criticism added greatly to the joy of writing.I would like to thank Don Zagier for introducing me to the subject of generalised Fermat equations, Bjorn Poonen for introducing me to effective Chabauty methods, Joe Wetherell for sharing covering techniques with me and Hendrik Lenstra for many sharp questions about the manuscript that helped improve it.Furthermore, I am deeply endebted to the KANT group in Berlin for the outstanding support they have given in using their software.Finally, I would like to thank all people at the Mathematisch