عنوان

Elliptic curves /

شابک

0387954902

شابک

1441930256

شابک

9780387954905

شابک

9781441930255

شماره

dltt

عنوان اصلي

Elliptic curves /

نام عام مواد

[Book]

نام نخستين پديدآور

Dale Husemöller ; with appendices by Stefan Theisen, Otto Forster, and Ruth Lawrence

وضعيت ويراست

Second edition

نام خاص و کميت اثر

xxi, 487 pages :

ساير جزييات

illustrations ;

ابعاد

25 cm

عنوان فروست

Graduate texts in mathematics ;

مشخصه جلد

111

متن يادداشت

Includes bibliographical references (pages 465-478) and index

متن يادداشت

Introduction to rational points on plane curves -- Elementary properties of chord-tangent group law on a cubic curve -- Plane algebraic curves -- Elliptic curves and their isomorphisms -- Families of elliptic curves and geometric properties of Torsion points -- Reduction mod p and torsion points -- Proof of Mordell's finite generation theorem -- Galois cohomology and isomorphism classification of elliptic curves over arbitrary fields -- Descent and Galois cohomology -- Elliptic and hypergeometric functions -- Theta functions -- Modular functions -- Endomorphisms of elliptic curves -- Elliptic curves over finite fields -- Elliptic curves over local fields -- Elliptic curves over global fields and ℓ-adic representations -- L-function of an elliptic curve and its analytic continuation -- Remarks on the Birch and Swinnerton-Dyer conjecture -- Remarks on the modular elliptic curves conjecture and Fermat's last theorem -- Higher dimensional analogs of elliptic curves: Calabi-Yau varieties -- Families of elliptic curves -- Appendix I: Calabi-Yau manifolds and string theory -- Appendix II: Elliptic curves in algorithmic number theory and cryptography -- Appendix III: Elliptic curves and topological modular forms -- Appendix IV: Guide to the exercises

بدون عنوان

0

متن يادداشت

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

موضوع مستند نشده

Curves, Algebraic

موضوع مستند نشده

Curves, Elliptic

موضوع مستند نشده

Group schemes (Mathematics)

موضوع مستند نشده

Courbes algébriques

موضوع مستند نشده

Courbes elliptiques

موضوع مستند نشده

Schémas en groupes - Mathématiques

موضوع مستند نشده

QA

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Husemöller, Dale

تاريخ عمليات

20160712072444.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y