Lectures on elliptic curves /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Cassels, J. W. S. (John William Scott)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, 1991.
Colección:London Mathematical Society student texts ; 24.
Temas:
Curves, Elliptic.
Courbes elliptiques.
MATHEMATICS > Geometry > Algebraic.
Diophantische Gleichung
Elliptische Kurve
Elliptische functies.
Elliptiske kurver.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1 Curves of genus 0. Introduction 3
  • 2 p-adic numbers 6
  • 3 Local-global principle for conics 13
  • 4 Geometry of numbers 17
  • 5 Local-global principle. Conclusion of proof 20
  • 6 Cubic curves 23
  • 7 Non-singular cubics. The group law 27
  • 8 Elliptic curves. Canonical form 32
  • 9 Degenerate laws 39
  • 10 Reduction 42
  • 11 P-adic case 46
  • 12 Global torsion 50
  • 13 Finite basis theorem. Strategy and comments 54
  • 14 A 2-isogeny 58
  • 15 Weak finite basis theory 66
  • 16 Remedial mathematics. Resultants 75
  • 17 Heights. Finite basis Theorem 78
  • 18 Local-global for genus 1 85
  • 19 Elements of Galois cohomology 89
  • 20 Construction of the jacobian 92
  • 21 Some abstract nonsense 98
  • 22 Principal homogeneous spaces and Galois cohomology 104
  • 23 Tate-Shafarevich group 108
  • 24 Endomorphism group 114
  • 25 Points over finite fields 118
  • 26 Factorizing using elliptic curves 124.

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