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Download E-books Rational Points on Modular Elliptic Curves (Cbms Regional Conference Series in Mathematics) PDF

By Henri Darmon

The e-book surveys a few contemporary advancements within the mathematics of modular elliptic curves. It areas a different emphasis at the building of rational issues on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the an important position performed by means of modularity in laying off gentle on those heavily similar concerns. the most subject of the publication is the idea of complicated multiplication, Heegner issues, and a few conjectural editions. the 1st 3 chapters introduce the heritage and conditions: elliptic curves, modular kinds and the Shimura-Taniyama-Weil conjecture, complicated multiplication and the Heegner aspect development. the following 3 chapters introduce versions of modular parametrizations during which modular curves are changed by means of Shimura curves hooked up to sure indefinite quaternion algebras. the most new contributions are present in Chapters 7-9, which survey the author's makes an attempt to increase the speculation of Heegner issues and intricate multiplication to occasions the place the bottom box isn't really a CM box. bankruptcy 10 explains the evidence of Kolyvagin's theorem, which relates Heegner issues to the mathematics of elliptic curves and ends up in the simplest proof to date for the Birch and Swinnerton-Dyer conjecture.

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