03242nmm a2200289 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002100139245006500160250001700225260004800242300003100290505092200321653002601243653001301269653002701282710003401309041001901343989003801362490003401400856007201434082000801506520143801514EB000632044EBX0100000000000000048512600000000000000.0cr|||||||||||||||||||||140122 ||| eng a97814757511921 aHusemoller, Dale00aElliptic CurveshElektronische Ressourcecby Dale Husemoller a1st ed. 1987 aNew York, NYbSpringer New Yorkc1987, 1987 aXV, 350 pbonline resource0 ato 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 Mordellâ€™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 aMathematical analysis aAnalysis aAnalysis (Mathematics)2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aGraduate Texts in Mathematics uhttps://doi.org/10.1007/978-1-4757-5119-2?nosfx=yxVerlag3Volltext0 a515 aThis 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