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ELLIPTIC CURVES (M2, Husemoller)

Lecture Topic : (Pure Math) ELLIPTIC CURVES (M2, Husemoller)

Prerequisites : Homology/Cohomology (M2);

Recommended Text(s) :

“Elliptic Curves”, 2nd Edn., Graduate Texts in Mathematics (GTM) No. 111, Dale Husemoller, Springer, 2004.

Approx price new on Amazon.com (hard copy) : $70

Approx price second hand on Amazon.com (hard copy) : $81

Availability free on eMule.com (e-format) : yes?

eMule search key word(s) : Husemoller, Elliptic Curves

Lectures and Links :

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Lecture 0  (link)

Ch.0   Introduction to Rational Points on Plane Curves

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Lecture 1  (link)

Ch.1   Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve

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Lecture 2  (link)

Ch.2   Plane Algebraic Curves

Appendix to Ch.2 : Factorial Rings and Elimination Theory

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Lecture 3  (link)

Ch.3   Elliptic Curves and Their Isomorphisms

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Lecture 4 (link)

Ch.4   Families of Elliptic Curves and Geometric Properties of Torsion Points

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Lecture 5  (link)

Ch.5   Reduction mod p and Torsion Points

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Lecture 6  (link)

Ch.6   Proof of Mordell’s Finite Generation Theorem

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Lecture 7  (link)

Ch.7   Galois Cohomology and Isomorphism Classification of Elliptic Curves Over Arbitrary Fields

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Lecture 8  (link)

Ch.8   Descent and  Galois Cohomology

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Lecture 9  (link)

Ch.9   Elliptic and Hypergeometric Functions

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Lecture 10  (link)

Ch.10   Theta Functions

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Lecture 11  (link)

Ch.11   Modular Functions

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Lecture 12  (link)

Ch.12   Endomorphisms of Elliptic Curves

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Lecture 13  (link)

Ch.13   Elliptic Curves Over Finite Fields

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Lecture 14  (link)

Ch.14   Elliptic Curves Over Local Fields

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Lecture 15  (link)

Ch.15   Elliptic Curves Over Global Fields and L-Adic Representations

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Lecture 16  (link)

Ch.16   L-Function of an Elliptic Curve and Its Analytic Continuation

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Lecture 17  (link)

Ch.17   Remarks on the Birch and Swinnerton-Dyer Conjecture

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Lecture 18  (link)

Ch.18   Remarks on the Modular Elliptic Curves Conjecture and Fermat’s Last Theorem

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Lecture 19  (link)

Ch.19   Higher Dimensional Analogs of Elliptic Curves : Calabi-Yau Varieties

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Lecture 20  (link)

Ch.20   Families of Elliptic Curves

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Lecture 21  (link)

Appendix 1 : Calabi-Yau Manifolds and String Theory

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Lecture 22  (link)

Appendix 2 : Elliptic Curves in Algorithmic Number Theory and Cryptography

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Lecture 23  (link)

Appendix 3 : Elliptic Curves and Topological Modular Forms

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Lecture 24  (link)

Appendix 4 : Guide to the Exercises

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