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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 (hard copy) : $70

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

Availability free on (e-format) : yes?

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

Lectures and Links :


Lecture 0  (link)

Ch.0   Introduction to Rational Points on Plane Curves


Lecture 1  (link)

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


Lecture 2  (link)

Ch.2   Plane Algebraic Curves

Appendix to Ch.2 : Factorial Rings and Elimination Theory


Lecture 3  (link)

Ch.3   Elliptic Curves and Their Isomorphisms


Lecture 4 (link)

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


Lecture 5  (link)

Ch.5   Reduction mod p and Torsion Points


Lecture 6  (link)

Ch.6   Proof of Mordell’s Finite Generation Theorem


Lecture 7  (link)

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


Lecture 8  (link)

Ch.8   Descent and  Galois Cohomology


Lecture 9  (link)

Ch.9   Elliptic and Hypergeometric Functions


Lecture 10  (link)

Ch.10   Theta Functions


Lecture 11  (link)

Ch.11   Modular Functions


Lecture 12  (link)

Ch.12   Endomorphisms of Elliptic Curves


Lecture 13  (link)

Ch.13   Elliptic Curves Over Finite Fields


Lecture 14  (link)

Ch.14   Elliptic Curves Over Local Fields


Lecture 15  (link)

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


Lecture 16  (link)

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


Lecture 17  (link)

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


Lecture 18  (link)

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


Lecture 19  (link)

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


Lecture 20  (link)

Ch.20   Families of Elliptic Curves


Lecture 21  (link)

Appendix 1 : Calabi-Yau Manifolds and String Theory


Lecture 22  (link)

Appendix 2 : Elliptic Curves in Algorithmic Number Theory and Cryptography


Lecture 23  (link)

Appendix 3 : Elliptic Curves and Topological Modular Forms


Lecture 24  (link)

Appendix 4 : Guide to the Exercises


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