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.
Read Online or Download Rational Points on Modular Elliptic Curves (Cbms Regional Conference Series in Mathematics) PDF
Best Algebraic Geometry books
The Iranian revolution nonetheless baffles such a lot Western observers. Few thought of the increase of theocracy in a modernized nation attainable, and less idea it may well end result from a well-liked revolution. acknowledged Amir Arjomand's The Turban for the Crown presents a considerate, painstakingly researched, and intelligible account of the turmoil in Iran which finds the significance of this singular occasion for our knowing of revolutions.
First textbook-level account of easy examples and strategies during this quarter. appropriate for self-study via a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a widely known mathematician and present president of the yankee Mathematical Society, in addition to a winning Springer writer.
This e-book introduces the idea of modular varieties, from which all rational elliptic curves come up, with a watch towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner conception; Hecke eigenforms and their mathematics houses; the Jacobians of modular curves and the Abelian kinds linked to Hecke eigenforms.
In response to a direction given to gifted high-school scholars at Ohio collage in 1988, this publication is largely a sophisticated undergraduate textbook in regards to the arithmetic of fractal geometry. It properly bridges the space among conventional books on topology/analysis and extra really good treatises on fractal geometry.
Extra info for Rational Points on Modular Elliptic Curves (Cbms Regional Conference Series in Mathematics)