Geometric Modular Forms and Elliptic Curves - Rilegato

Hida, Haruzo

Rilegato

ISBN 10: 9810243375 ISBN 13: 9789810243371

Casa editrice: World Scientific Pub Co Inc, 2000

Riassunto

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura–Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction.In this new second edition, a detailed description of Barsotti–Tate groups (including formal Lie groups) is added to Chapter 1. As an application, a down-to-earth description of formal deformation theory of elliptic curves is incorporated at the end of Chapter 2 (in order to make the proof of regularity of the moduli of elliptic curve more conceptual), and in Chapter 4, though limited to ordinary cases, newly incorporated are Ribet's theorem of full image of modular p-adic Galois representation and its generalization to 'big' ?-adic Galois representations under mild assumptions (a new result of the author). Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian Q-varieties and Q-curves).

Su questo libro

Recensione

" ... this is a welcome addition to the literature in a field difficult to penetrate. This book should obviously be carefully studied by advanced students and by professional mathematicians in arithmetic algebraic geometry or (modern) number theory."Mathematical Reviews-- "Geometric Modular Forms and Elliptic Curves is suited for both the (advanced and specialized) classroom and (well-prepared and highly motivated) reader bent of serious self-study. Beyond this, the book's prose is clear, there are examples and exercises available, and, as always, the serious student should have a go at them: he will reap wonderful benefits." --MAA Reviews

Product Description

Book by Haruzo Hida

Dettagli dell?edizione

• Editore: World Scientific Pub Co Inc
• Data di pubblicazione: 2000
• ISBN 10: 9810243375
• ISBN 13: 9789810243371
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero di pagine: 361
• Contatto del produttore: non disponibile