Elliptic Curves

AvDale Husemöller

Inbunden, Engelska, 2003

Del i serien Graduate Texts in Mathematics

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Beskrivning

This book is an introduction to the theory of elliptic curves, ranging from its most elementary aspects to current research. The first part, which grew out of Tate's Haverford lectures, covers the elementary arithmetic theory of elliptic curves over the rationals. The next two chapters recast the arguments used in the proof of the Mordell theorem into the context of Galois cohomology and descent theory. This is followed by three chapters on the analytic theory of elliptic curves, including such topics as elliptic functions, theta functions, and modular functions. Next, the theory of endomorphisms and elliptic curves over infinite and local fields are discussed. The book concludes with three chapters surveying recent results in the arithmetic theory, especially those related to the conjecture of the Birch and Swinnerton-Dyer. This new edition contains three new chapters and the addition of two appendices by Stefan Theisen and Otto Forster. Dale Husemoller is a member of the faculty at the Max Planck Institute of Mathematics.

Produktinformation

Utgivningsdatum:2003-12-22
Mått:155 x 235 x 35 mm
Vikt:923 g
Format:Inbunden
Språk:Engelska
Serie:Graduate Texts in Mathematics
Antal sidor:490
Upplaga:2
Förlag:Springer-Verlag New York Inc.
ISBN:9780387954905

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Recensioner i media

From the reviews of the second edition: "Husemoller's text was and is the great first introduction to the world of elliptic curves ... and a good guide to the current research literature as well. ... this second edition builds on the original in several ways. ... it has certainly gained a good deal of topicality, appeal, power of inspiration, and educational value for a wider public. No doubt, this text will maintain its role as both a useful primer and a passionate invitation to the evergreen theory of elliptic curves and their applications" (Werner Kleinert, Zentralblatt MATH, Vol. 1040, 2004)

Innehållsförteckning

to Rational Points on Plane Curves.- Elementary Properties of the 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 ?-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.