Modular curves and unramified extensions of number fields

S. Kamienny

Compositio Mathematica (1982)

  • Volume: 47, Issue: 2, page 223-235
  • ISSN: 0010-437X

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Kamienny, S.. "Modular curves and unramified extensions of number fields." Compositio Mathematica 47.2 (1982): 223-235. <http://eudml.org/doc/89572>.

@article{Kamienny1982,
author = {Kamienny, S.},
journal = {Compositio Mathematica},
keywords = {modular curves; unramified extensions of number fields; Bernoulli numbers; ideal class groups; Eisenstein prime},
language = {eng},
number = {2},
pages = {223-235},
publisher = {Martinus Nijhoff Publishers},
title = {Modular curves and unramified extensions of number fields},
url = {http://eudml.org/doc/89572},
volume = {47},
year = {1982},
}

TY - JOUR
AU - Kamienny, S.
TI - Modular curves and unramified extensions of number fields
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 47
IS - 2
SP - 223
EP - 235
LA - eng
KW - modular curves; unramified extensions of number fields; Bernoulli numbers; ideal class groups; Eisenstein prime
UR - http://eudml.org/doc/89572
ER -

References

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  1. [1] P. Deligne and N. Rapoport: Schémas de modules de courbes elliptiques. Lecture Notes in Mathematics349, Berlin -Heidelberg-New York, Springer-Verlag, 1973. Zbl0281.14010MR337993
  2. [2] M. Demazure: Lectures on p-divisible groups. Lecture Notes in Mathematics302, Berlin- Heidelberg-New York, Springer-Verlag, 1972. Zbl0247.14010MR883960
  3. [3] N. Katz: p-adic properties of modular schemes and modular forms, Vol. III of the Proceedings of the International Summer School on Modular Functions, Antwerp, 1972. Lecture Notes in Mathematics350, Berlin- Heidelberg-New York, Springer-Verlag, 1973. Zbl0271.10033MR447119
  4. [4] S. Kamienny: Harvard Ph.D. Thesis (December 1980). 
  5. [5] S. Kamienny and G. Stevens: Special values of L-functions attached to X1(N), to appear. Zbl0519.14018
  6. [6] D. Kubert and S. Lang: Modular Units, Berlin-Heidelberg -New York, Springer-Verlag, 1981. Zbl0492.12002MR648603
  7. [7] S. Lang: Introduction to modular forms, Berlin- Heidelberg-New York, Springer-Verlag, 1976. Zbl0344.10011MR429740
  8. [8] B. Mazur: Modular curves and the Eisenstein ideal. Publications Mathematiques I.H.E.S.47 (1978). 
  9. [9] B. Mazur: Rational isogenies of prime degree. Inv. Math.44 (1978) 129-162. Zbl0386.14009MR482230
  10. [10] B. Mazur and J. Tate: Points of Order 13 on elliptic curves. Inv. Math.22 (1973) 41-49. Zbl0268.14009MR347826
  11. [11] B. Mazur and A. Wiles: Class fields of abelian extensions of Q, in preparation. Zbl0545.12005
  12. [12] M. Raynaud: Schémas en groupes de type (p,..., p). Bull. Soc. Math. France102 (1974) 241-280. Zbl0325.14020MR419467
  13. [13] K. Ribet: A modular construction of unramified p-extensions of Q(μp). Inv. Math.34 (1976) 151-162. Zbl0338.12003
  14. [14] J.-P. Serre: Abelian l-adic representations and elliptic curves. Lectures at McGill University, New York- Amsterdam, W.A. Benjamin, Inc., 1968. Zbl0186.25701MR263823
  15. [15] J.-P. Serre and J. Tate: Good reduction of abelian varieties. Ann. of Math.88 (1968) 492-517. Zbl0172.46101MR236190
  16. [16] G. Shimura: Introduction to the arithmetic theory of automorphic Forms. Publ. Math. Soc. Japan11, Tokyo-Princeton, 1971. Zbl0221.10029MR314766
  17. [17] A. Wiles: Modular curves and the class group of Q(ζ p). Inv. Math.58 (1980) 1-35. Zbl0436.12004

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