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Modularity and Generalized Fermat's Equation de Dinesh Thakur

Modularity and Generalized Fermat's Equation: Contemporary Mathematics

Editat de Dinesh Thakur, Henri Darmon, Michael Bennett, Samir Siksek, Sujatha Ramdorai
en Limba Engleză Paperback – 11 noi 2026
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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Specificații

ISBN-13: 9781470485535
ISBN-10: 1470485532
Pagini: 317
Dimensiuni: 178 x 254 mm
Editura: American Mathematical Society
Colecția Contemporary Mathematics
Seria Contemporary Mathematics

Notă biografică

Michael Bennett, University of British Columbia, Vancouver, Canada, Henri Darmon, McGill University, Montreal, Canada, Sujatha Ramdorai, University of British Columbia, Vancouver, Canada, Samir Siksek, University of Warwick, Coventry, England, Dinesh Thakur, University of Rochester, New York, and Devendra Tiwari, Formerly of Bhaskaracharya Pratishthan, Pune, India

Cuprins

B. Sury, The role of elliptic curves and modular forms in Fermat's last theorem: A beginner's guide
  • Philippe Michaud-Jacobs, Mazur's isogeny theorem
  • Barinder S. Banwait, Modularity of $\mathbb{C}$ implies modularity over $\mathbb{Q}$
  • Mihir Sheth, The Eichler-Shimura relation
  • Ehsan Shahoseini, Deformation theory of Galois representations and the Taylor-Wiles method
  • Subham Bhakta, Srilakshmi Krishnamoorthy, and Sunil Kumar Pasupulati, Modular degree and a conjecture of Watkins
  • Pilar Bayer, Exploring Shimura curves through algorithmic methods
  • Ajith Nair and Ajmain Yamin, Hilbert modular forms and Galois representations
  • Nicolas Billerey, Introduction to the modular method
  • Maleeha Khawaja and Samir Siksek, The modular approach to Diophantine equations over totally real fields
  • William Y. Chen, Noncongruence modular curves as Hurwitz spaces
  • Imin Chen and Angelos Koutsianas, Darmon's program: A survey
  • Anand Deopurkar, The arithmetic and geometry of branched coverings: Theorems of Belyi and Darmon-Granville
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