---

＜電子ブック＞
Elliptic Curves / by Dale Husemoller
(Graduate Texts in Mathematics. ISSN:21975612 ; 111)

版	1st ed. 1987.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1987
本文言語	英語
大きさ	XV, 350 p : online resource
冊子体	Elliptic curves / Dale Husemöller ; with an appendix by Ruth Lawrence ; : us,: gw
著者標目	*Husemoller, Dale author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis FREE:Analysis
一般注記	to Rational Points on Plane Curves -- 1 Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve -- 2 Plane Algebraic Curves -- 3 Elliptic Curves and Their Isomorphisms -- 4 Families of Elliptic Curves and Geometric Properties of Torsion Points -- 5 Reduction mod p and Torsion Points -- 6 Proof of Mordell’s Finite Generation Theorem -- 7 Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields -- 8 Descent and Galois Cohomology -- 9 Elliptic and Hypergeometric Functions -- 10 Theta Functions -- 11 Modular Functions -- 12 Endomorphisms of Elliptic Curves -- 13 Elliptic Curves over Finite Fields -- 14 Elliptic Curves over Local Fields -- 15 Elliptic Curves over Global Fields and ?-Adic Representations -- 16 L-Function of an Elliptic Curve and Its Analytic Continuation -- 17 Remarks on the Birch and Swinnerton-Dyer Conjecture -- Appendix Guide to the Exercises 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4757-5119-2

 類似資料