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7. Finiteness of Tate-Shafarevich groups

  • Martin L. BrownEmail author
Chapter
  • 598 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1849)

Contents.

  • 7.1. Quasi-modules

  • 7.2. Igusa’s theorem

  • 7.3. Consequences of Igusa’s theorem

  • 7.4. Proof of proposition 7.3.6.

  • 7.5. Preliminaries

  • 7.6. Statement of the main result and historical remarks

  • 7.7. Tate-Shafarevich groups

  • 7.8. Proof that theorem 7.7.5 implies theorem 7.6.5

  • 7.9. The Selmer group

  • 7.10. The set \(\cal P\) of prime numbers

  • 7.11. Frobenius elements and the set \({\cal D}_{l^n}\) of divisors

  • 7.12. The Heegner module attached to E/F

  • 7.13. Galois invariants of the Heegner module and the map \(\eta \)

  • 7.14. The cohomology classes \(\gamma (c),\delta (c)\)

  • 7.15. Tate-Poitou local duality

  • 7.16. Application of Tate-Poitou duality

  • 7.17. Equivariant Pontrjagin duality

  • 7.18. Proof of theorem 7.7.5

  • 7.19. Comments and errata for [Br2]

Mathematics Subject Classification (2000):

11F52 11G05 11G09 11G15 11G40 11R58 14F20 14G10 14H52 14J27 14K22 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Institut FourierSaint-Martin d’HèresFrance

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