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Synopsis
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.
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Review
"... 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
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GEOMETRIC MODULAR FORMS AND ELLIPTIC CURVES
Published by
World Scientific Publishing Company, 2001
ISBN 10: 9810243375
ISBN 13: 9789810243371
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Geometric Modular Forms And Elliptic Curves
Published by
World Scientific Publishing Company, 2001
ISBN 10: 9810243375
ISBN 13: 9789810243371
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Geometric Modular Forms and Elliptic Curves
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