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The Arithmetic of Elliptic Curves (Hardcover, 2nd ed. 2009)
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The Arithmetic of Elliptic Curves (Hardcover, 2nd ed. 2009)
Series: Graduate Texts in Mathematics, 106
Expected to ship within 12 - 17 working days
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The theory of elliptic curves is distinguished by its long history
and by the diversity of the methods that have been used in its
study. This book treats the arithmetic approach in its modern
formulation, through the use of basic algebraic number theory and
algebraic geometry. Following a brief discussion of the necessary
algebro-geometric results, the book proceeds with an exposition of
the geometry and the formal group of elliptic curves, elliptic
curves over finite fields, the complex numbers, local fields, and
global fields. Final chapters deal with integral and rational
points, including Siegels theorem and explicit computations for the
curve Y = X + DX, while three appendices conclude the whole:
Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and
an overview of more advanced topics.
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