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140122  eng 
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a 9781475751192

100 
1 

a Husemoller, Dale

245 
0 
0 
a Elliptic Curves
h Elektronische Ressource
c by Dale Husemoller

250 


a 1st ed. 1987

260 


a New York, NY
b Springer New York
c 1987, 1987

300 


a XV, 350 p
b online resource

505 
0 

a to Rational Points on Plane Curves  1 Elementary Properties of the ChordTangent 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 LFunction of an Elliptic Curve and Its Analytic Continuation  17 Remarks on the Birch and SwinnertonDyer Conjecture  Appendix Guide to the Exercises

653 


a Mathematical analysis

653 


a Analysis

653 


a Analysis (Mathematics)

710 
2 

a SpringerLink (Online service)

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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0 

a Graduate Texts in Mathematics

856 


u https://doi.org/10.1007/9781475751192?nosfx=y
x Verlag
3 Volltext

082 
0 

a 515

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a 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 SwinnertonDyer. 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 higherdimensional analogues of elliptic curves, including K3 surfaces and CalabiYau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of CalabiYau 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
