Elliptic curves.
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| Author / Creator: | Husemöller, Dale. |
|---|---|
| Edition: | 2nd ed. / Dale Husemöller ; with appendices by Otto Forster, Ruth Lawrence, and Stefan Theisen. |
| Imprint: | New York : Springer, c2004. |
| Description: | xxi, 487 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Graduate texts in mathematics ; 111 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5058946 |
Table of Contents:
- Introduction to Rational Points on Plane Curves
- 1. Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve
- 2. Plane Algebraic Curves
- App. to Ch. 2. Factorial Rings and Elimination Theory
- 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 l-Adic Representations
- 16. L-Function of an Elliptic Curve and Its Analytic Continuation
- 17. Remarks on the Birch and Swinnerton-Dyer Conjecture
- 18. Remarks on the Modular Elliptic Curves Conjecture and Fermat's Last Theorem
- 19. Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties
- 20. Families of Elliptic Curves
- App. I. Calabi-Yau Manifolds and String Theory / Stefan Theisen
- App. II. Elliptic Curves in Algorithmic Number Theory and Cryptography / Otto Forster
- App. III. Elliptic Curves and Topological Modular Forms
- App. IV. Guide to the Exercises / Ruth Lawrence.