LMSST: 24 Lectures on Elliptic Curves

Häftad, Engelska, 1991

Del 24 i serien London Mathematical Society Student Texts

525 kr

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Beskrivning

The study of (special cases of) elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centres of research in number theory. This book, which is addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Weil finite basis theorem, points of finite order (Nagell-Lutz) etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the 'Riemann hypothesis for function fields') and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch, as is the little that is needed on Galois cohomology. Many examples and exercises are included for the reader. For those new to elliptic curves, whether they are graduate students or specialists from other fields, this will be a fine introductory text.

Produktinformation

Utgivningsdatum:1991-11-21
Mått:150 x 227 x 10 mm
Vikt:191 g
Format:Häftad
Språk:Engelska
Serie:London Mathematical Society Student Texts
Antal sidor:144
Förlag:Cambridge University Press
ISBN:9780521425308

Utforska kategorier

Matematik inom Naturvetenskap och teknik
Talteori inom Naturvetenskap och teknik

Recensioner i media

'… an excellent introduction … written with humour.' Monatshefte für Mathematik

Innehållsförteckning

Introduction; 1. Curves of genus: introduction; 2. p-adic numbers; 3. The local-global principle for conics; 4. Geometry of numbers; 5. Local-global principle: conclusion of proof; 6. Cubic curves; 7. Non-singular cubics: the group law; 8. Elliptic curves: canonical form; 9. Degenerate laws; 10. Reduction; 11. The p-adic case; 12. Global torsion; 13. Finite basis theorem: strategy and comments; 14. A 2-isogeny; 15. The weak finite basis theorem; 16. Remedial mathematics: resultants; 17. Heights: finite basis theorem; 18. Local-global for genus principle; 19. Elements of Galois cohomology; 20. Construction of the jacobian; 21. Some abstract nonsense; 22. Principle homogeneous spaces and Galois cohomology; 23. The Tate-Shafarevich group; 24. The endomorphism ring; 25. Points over finite fields; 26. Factorizing using elliptic curves; Formulary; Further reading; Index.

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LMSST: 24 Lectures on Elliptic Curves

AvJ. W. S. Cassels

Häftad, Engelska, 1991

Del 24 i serien London Mathematical Society Student Texts

525 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Beskrivning

Produktinformation

Utgivningsdatum:1991-11-21
Mått:150 x 227 x 10 mm
Vikt:191 g
Format:Häftad
Språk:Engelska
Serie:London Mathematical Society Student Texts
Antal sidor:144
Förlag:Cambridge University Press
ISBN:9780521425308

Utforska kategorier

Matematik inom Naturvetenskap och teknik
Talteori inom Naturvetenskap och teknik

Recensioner i media

'… an excellent introduction … written with humour.' Monatshefte für Mathematik

Innehållsförteckning

Introduction; 1. Curves of genus: introduction; 2. p-adic numbers; 3. The local-global principle for conics; 4. Geometry of numbers; 5. Local-global principle: conclusion of proof; 6. Cubic curves; 7. Non-singular cubics: the group law; 8. Elliptic curves: canonical form; 9. Degenerate laws; 10. Reduction; 11. The p-adic case; 12. Global torsion; 13. Finite basis theorem: strategy and comments; 14. A 2-isogeny; 15. The weak finite basis theorem; 16. Remedial mathematics: resultants; 17. Heights: finite basis theorem; 18. Local-global for genus principle; 19. Elements of Galois cohomology; 20. Construction of the jacobian; 21. Some abstract nonsense; 22. Principle homogeneous spaces and Galois cohomology; 23. The Tate-Shafarevich group; 24. The endomorphism ring; 25. Points over finite fields; 26. Factorizing using elliptic curves; Formulary; Further reading; Index.