楕円曲線（第２版） Elliptic Curves (Graduate Texts in Mathematics Vol.111) （2nd ed. 2004. XXI, 487 p. w. 42 figs. 24,5 cm）

Husemoller, Dale

SPRINGER, BERLIN（2004発売）

• 製本 Hardcover:ハードカバー版／ページ数 400 p.
• 商品コード 9780387954905

基本説明

An introduction to the theory of elliptic curves, ranging from its most elementary aspects to current research. Concludes with three chapters surveying recent results in the arithmetic theory, especially those related to the conjecture of the Birch and Swinnerton-Dyer.

Full Description

There are three new appendices, one by Stefan Theisen on the role of Calabi- Yau manifolds in string theory and one by Otto Forster on the use of elliptic curves in computing theory and coding theory. In the third appendix we discuss the role of elliptic curves in homotopy theory. In these three introductions the reader can get a clue to the far-reaching implications of the theory of elliptic curves in mathematical sciences. During the ?nal production of this edition, the ICM 2002 manuscript of Mike Hopkins became available. This report outlines the role of elliptic curves in ho- topy theory. Elliptic curves appear in the form of the Weierstasse equation and its related changes of variable. The equations and the changes of variable are coded in an algebraic structure called a Hopf algebroid, and this Hopf algebroid is related to a cohomology theory called topological modular forms. Hopkins and his coworkers have used this theory in several directions, one being the explanation of elements in stable homotopy up to degree 60. In the third appendix we explain how what we described in Chapter 3 leads to the Weierstrass Hopf algebroid making a link with Hopkins' paper.