Rational points on modular elliptic curves
著者
書誌事項
Rational points on modular elliptic curves
（Regional conference series in mathematics, no. 101）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society with support from the National Science Foundation, c2004
大学図書館所蔵 件 / 全48件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
"This monograph is based on an NSF-CBMS lecture series given by the author at the University of Central Florida in Orlando from August 8 to 12, 2001."--Pref
Includes bibliographical references (p. 125-129)
内容説明・目次
内容説明
This book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras.The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
目次
Elliptic curves Modular forms Heegner points on $X_0(N)$ Heegner points on Shimura curves Rigid analytic modular forms Rigid analytic modular parametrisations Totally real fields ATR points Integration on $\mathcal{H}_p\times\mathcal{H}$ Kolyvagin's theorem Bibliography.
「Nielsen BookData」 より
