Advanced Topics in the Arithmetic of Elliptic Curves

Released on by Joseph H. Silverman
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  • Advanced Topics in the Arithmetic of Elliptic Curves Book Detail

  • Author : Joseph H. Silverman
  • Release Date : 2013-12-01
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 482
  • ISBN 13 : 1461208513
  • File Size : 40,40 MB
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Advanced Topics in the Arithmetic of Elliptic Curves by Joseph H. Silverman PDF Summary

Book Description: In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.

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