Selmer groups and Heegner points in anticyclotomic p -extensions

Massimo Bertolini

Compositio Mathematica (1995)

  • Volume: 99, Issue: 2, page 153-182
  • ISSN: 0010-437X

How to cite

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Bertolini, Massimo. "Selmer groups and Heegner points in anticyclotomic $\mathbb {Z}_p$-extensions." Compositio Mathematica 99.2 (1995): 153-182. <http://eudml.org/doc/90412>.

@article{Bertolini1995,
author = {Bertolini, Massimo},
journal = {Compositio Mathematica},
keywords = {anticyclotomic -extension; modular elliptic curve; Heegner hypothesis; Iwasawa algebra; Heegner points; Selmer group; Iwasawa theory},
language = {eng},
number = {2},
pages = {153-182},
publisher = {Kluwer Academic Publishers},
title = {Selmer groups and Heegner points in anticyclotomic $\mathbb \{Z\}_p$-extensions},
url = {http://eudml.org/doc/90412},
volume = {99},
year = {1995},
}

TY - JOUR
AU - Bertolini, Massimo
TI - Selmer groups and Heegner points in anticyclotomic $\mathbb {Z}_p$-extensions
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 99
IS - 2
SP - 153
EP - 182
LA - eng
KW - anticyclotomic -extension; modular elliptic curve; Heegner hypothesis; Iwasawa algebra; Heegner points; Selmer group; Iwasawa theory
UR - http://eudml.org/doc/90412
ER -

References

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  1. 1 Bertolini, M.: Iwasawa Theory, L-functions and Heegner Points, PhD Thesis, Columbia University, 1992. 
  2. 2 Bertolini, M. and Darmon, H.: Kolyvagin's descent and Mordell-Weil groups over ring class fields, J. für die Reine und Angewandte Mathematik412 (1990), 63-74. Zbl0712.14008MR1079001
  3. 3 Bertolini, M. and Darmon, H.: Derived heights and generalized Mazur-Tate regulators, Duke Math. J.76 (1994), 75-111. Zbl0853.14013MR1301187
  4. 4 Bertolini, M. and Darmon, H.: Derived p-adic heights, submitted. 
  5. 5 Bourbaki, N.: Algèbre Commutative, Ch.7, Diviseurs, Hermann et Co., Paris, 1965. Zbl0141.03501MR260715
  6. 6 Darmon, H.: Refined Class Number Formulas and Derivatives of L-functions, PhD Thesis, Harvard University, 1991. 
  7. 7 Cassels, J.W.S. and Frölich, A.: Algebraic Number Theory, Academic Press, New York, 1969. Zbl0153.07403MR215665
  8. 8 Gross, B.H.: Kolyvagin's work on modular elliptic curves, in L-functions and Arithmetic, Cambridge University Press, Cambridge, 1991, pp. 235-256. Zbl0743.14021MR1110395
  9. 9 Gross, B.H. and Zagier, D.: Heegner points and derivatives of L-series, Inventiones Math.84 (1986), 225-320. Zbl0608.14019MR833192
  10. 10 Kolyvagin, V.A.: Euler Systems, The Grothendieck Festschrift, vol. 2, Progr. in Math. 87, Birkhäuser, 1990, pp. 435-483. Zbl0742.14017MR1106906
  11. 11 Lang, S.: Algebra, 2nd edn, Addison Wesley, 1984. Zbl0712.00001
  12. 12 Mazur, B.: Modular Curves and Arithmetic, Proc. Int. Congress of Math., Warszawa, 1983. Zbl0597.14023
  13. 13 Mazur, B.: Rational points of Abelian Varieties with values in towers of number fields, Inventiones Math.18 (1972), 183-266. Zbl0245.14015MR444670
  14. 14 Manin, Ju.: Cyclotomic fields and modular curves. Engl. transl.: Russian Math. Surveys26 (1971), 7-78. Zbl0266.14012MR401653
  15. 15 Milne, J.S.: Arithmetic duality theorems, in Perspective in Math., Academic Press, New York, 1986. Zbl0613.14019MR881804
  16. 16 Perrin-Riou, B.: Fonctions L p-adiques, Théorie d'Iwasawa et points de Heegner, Bull. Soc. Math. de France115 (1987), 399-456. Zbl0664.12010MR928018
  17. 17 Perrin-Riou, B.: Points de Heegner et derivées de fonctions L p-adiques, Inventiones Math.89 (1987), 455-510. Zbl0645.14010MR903381
  18. 18 Rohrlich, D.: On L-functions of elliptic curves and anti-cyclotomic towers, Inventiones Math.64 (1984), 383-408. Zbl0565.14008MR735332
  19. 19 Rubin, K.C.: The Main Conjecture, Appendix in S. Lang, Cyclotomic fields, I and II, GTM 121, Springer-Verlag, 1990. Zbl0704.11038
  20. 20 Rubin, K.C.: The "main conjectures" of Iwasawa theory for imaginary quadratic fields, Inventiones Math. 103 (1991), 25-68. Zbl0737.11030MR1079839
  21. 21 Serre, J.P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Inventiones Math.15 (1972), 259-331. Zbl0235.14012MR387283
  22. 22 Serre, J.P.: Abelian l-adic Representations and Elliptic Curves, Advanced Book Classics, Addison Wesley, 1989. Zbl0709.14002MR1043865
  23. 23 Tate, J.: WC-groups over p-adic Fields, Séminaire Bourbaki no. 156, 1957. Zbl0091.33701MR105420
  24. 24 Tate, L.: Duality theorems in Galois cohomology over number fields, in Proc. Int. Congress of Math., Stockholm, 1962, pp. 288-295. Zbl0126.07002MR175892

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