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

By Henri Darmon

The booklet 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 via modularity in laying off gentle on those heavily similar matters. the most subject matter of the e-book is the speculation of advanced multiplication, Heegner issues, and a few conjectural versions. the 1st 3 chapters introduce the historical past and conditions: elliptic curves, modular types and the Shimura-Taniyama-Weil conjecture, advanced multiplication and the Heegner aspect building. the subsequent 3 chapters introduce versions of modular parametrizations within 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 idea 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 results in the easiest proof to date for the Birch and Swinnerton-Dyer conjecture.

Show description

Read or Download Rational Points on Modular Elliptic Curves (Cbms Regional Conference Series in Mathematics) PDF

Similar Algebraic Geometry books

Homotopy Type and Homology (Oxford Mathematical Monographs)

The writer, a number one determine in algebraic topology, offers a latest therapy of an extended confirmed set of questions during this vital examine region. The book's central objective--and major result--is the class theorem on k-variants and boundary invariants, which complement the classical photograph of homology and homotopy teams, in addition to computations of varieties which are got through utilizing this theorem.

Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics)

In response to a direction given to proficient high-school scholars at Ohio college in 1988, this ebook is largely a complicated undergraduate textbook concerning the arithmetic of fractal geometry. It properly bridges the space among conventional books on topology/analysis and extra really expert treatises on fractal geometry.

Modular Forms and Fermat's Last Theorem

This quantity includes the elevated lectures given at a convention on quantity thought and mathematics geometry held at Boston college. It introduces and explains the various principles and methods utilized by Wiles, and to provide an explanation for how his outcome could be mixed with Ribets theorem and concepts of Frey and Serre to end up Fermats final Theorem.

Additional info for Rational Points on Modular Elliptic Curves (Cbms Regional Conference Series in Mathematics)

Show sample text content

Rated 4.80 of 5 – based on 27 votes