Elliptic Curves and Big Galois Representations 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Delbourgo, Daniel 作者

译者

2008-7 出版日期

288 页数

$ 88.14 价格

丛书系列

9780521728669 图书编码

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Elliptic Curves and Big Galois Representations 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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The arithmetic properties of modular forms and elliptic curves lie at the heart of modern number theory. This book develops a generalisation of the method of Euler systems to a two-variable deformation ring. The resulting theory is then used to study the arithmetic of elliptic curves, in particular the Birch and Swinnerton-Dyer (BSD) formula. Three main steps are outlined: the first is to parametrise 'big' cohomology groups using (deformations of) modular symbols. Finiteness results for big Selmer groups are then established. Finally, at weight two, the arithmetic invariants of these Selmer groups allow the control of data from the BSD conjecture. As the first book on the subject, the material is introduced from scratch; both graduate students and professional number theorists will find this an ideal introduction. Material at the very forefront of current research is included, and numerical examples encourage the reader to interpret abstract theorems in concrete cases.

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