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portada Modularity and Generalized Fermat's Equation
Type
Physical Book
Publisher
Author
Collection
Contemporary Mathematics
Year
2026
Language
English
Pages
317
Format
Paperback
Dimensions
25.4x17.8 cm
ISBN13
9781470485535

Modularity and Generalized Fermat's Equation

Michael Bennett;Henri Darmon;Sujatha Ramdorai;Samir Siksek;Dinesh Thakur (Author) · American Mathematical Society · Paperback

Modularity and Generalized Fermat's Equation - Michael Bennett;Henri Darmon;Sujatha Ramdorai;Samir Siksek;Dinesh Thakur

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Synopsis "Modularity and Generalized Fermat's Equation"

This volume contains the detailed exposition of virtual lectures on the theme ""Modularity and Generalized Fermat's Equation"", which were delivered in January-April 2022 during the program organized by the Bhaskaracharya Pratishthan Research Institute in Mathematics, Pune, India. Modularity of elliptic curves over the field of rational numbers plays a central role in the proof of the celebrated Fermat's Last Theorem (FLT) by Wiles and Taylor-Wiles in 1995. Around the same time Henri Darmon and his collaborators initiated the study of Generalized Fermat Equations (GFE) in a series of papers. This work leads to an ambitious program to study the generalized Fermat equation $aX^m bY^n=cZ^r$ using the modularity of abelian varieties of $\mathrm{GL}_2$-type over totally real fields. This volume covers some of the background material and presents the current state of the art in this area.

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