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Advanced Topics in the Arithmetic of Elliptic Curves : Graduate Texts in Mathematics - Joseph H. Silverman

Advanced Topics in the Arithmetic of Elliptic Curves

By: Joseph H. Silverman

Paperback | 1 September 1999

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This book continues the treatment of the arithmetic theory of elliptic curves begun in the first volume. The book begins with the theory of elliptic and modular functions for the full modular group r(1), including a discussion of Hekcke operators and the L-series associated to cusp forms. This is followed by a detailed study of elliptic curves with complex multiplication, their associated Grossencharacters and L-series, and applications to the construction of abelian extensions of quadratic imaginary fields. Next comes a treatment of elliptic curves over function fields and elliptic surfaces, including specialization theorems for heights and sections. This material serves as a prelude to the theory of minimal models and Neron models of elliptic curves, with a discussion of special fibers, conductors, and Ogg's formula. Next comes a brief description of q-models for elliptic curves over C and R, followed by Tate's theory of q-models for elliptic curves with non-integral j-invariant over p-adic fields. The book concludes with the construction of canonical local height functions on elliptic curves, including explicit formulas for both archimedean and non-archimedean fields.
Industry Reviews
.,."this book deserves to be as popular as its forerunner and a great many people will be looking forward to reading a third volume." - Monatshefte fA1/4r Mathematik

You Can Find This Book In

Non-FictionMathematicsGeometryAlgebraic GeometryMathematical FoundationAlgebraNumber Theory

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Published: 4th November 1994

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