Download E-books The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) PDF

By Joseph H. Silverman

The speculation of elliptic curves is unique by means of its lengthy heritage and by way of the variety of the tools which were utilized in its research. This e-book treats the mathematics procedure in its glossy formula, by using simple algebraic quantity concept and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the booklet proceeds with an exposition of the geometry and the formal crew of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and international fields. ultimate chapters care for essential and rational issues, together with Siegels theorem and specific computations for the curve Y = X + DX, whereas 3 appendices finish the full: Elliptic Curves in features 2 and three, workforce Cohomology, and an outline of extra complex issues.

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