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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Geometric Modular Forms And Elliptic Curves (2nd Edition) (Hardcover, 2nd Revised edition)
Loot Price: R4,506
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Geometric Modular Forms And Elliptic Curves (2nd Edition) (Hardcover, 2nd Revised edition)
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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 -varieties and -curves).
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