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<p>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.</p> <p>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' Λ-adic Galois representations under mild assumptions (a new result of the author). Though some of recent striking developments is out of the scope of thi

Who reads Geometric Modular Forms and Elliptic Curves?

Author

Haruzo Hida

Publisher

World Scientific Pub Co Inc

Published

2001

Language

EN

ISBN

9789812792693

Category

nonfiction

Subjects

Mathematics, Stem