TY - CHAP

T1 - Appendix IV

T2 - Guide to the exercises

AU - Husemöller, Dale

AU - Forster, Otto

AU - Lawrence, Ruth

AU - Theisen, S

PY - 2004

Y1 - 2004

N2 - This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers. This theory is then recast into the powerful and more general language of Galois cohomology and descent theory. An analytic section of the book includes such topics as elliptic functions, theta functions, and modular functions. Next, the book discusses the theory of elliptic curves over finite and local fields and provides a survey of results in the global arithmetic theory, especially those related to the conjecture of Birch and Swinnerton-Dyer. This new edition contains three new chapters. The first is an outline of Wiles's proof of Fermat's Last Theorem. The two additional chapters concern higher-dimensional analogues of elliptic curves, including K3 surfaces and Calabi-Yau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of Calabi-Yau manifolds and elliptic curves in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory. About the First Edition: "All in all the book is well written, and can serve as basis for a student seminar on the subject." -G. Faltings, Zentralblatt.

AB - This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers. This theory is then recast into the powerful and more general language of Galois cohomology and descent theory. An analytic section of the book includes such topics as elliptic functions, theta functions, and modular functions. Next, the book discusses the theory of elliptic curves over finite and local fields and provides a survey of results in the global arithmetic theory, especially those related to the conjecture of Birch and Swinnerton-Dyer. This new edition contains three new chapters. The first is an outline of Wiles's proof of Fermat's Last Theorem. The two additional chapters concern higher-dimensional analogues of elliptic curves, including K3 surfaces and Calabi-Yau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of Calabi-Yau manifolds and elliptic curves in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory. About the First Edition: "All in all the book is well written, and can serve as basis for a student seminar on the subject." -G. Faltings, Zentralblatt.

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SN - 0387954902

SN - 9780387954905

T3 - Graduate texts in mathematics

BT - Elliptic curves

PB - Springer

CY - New York

ER -