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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

The torsion of $ p$-ramified Iwasawa modules II

Author(s): Satoshi Fujii
Journal: Proc. Amer. Math. Soc. 136 (2008), 461-466.
MSC (2000): Primary 11R23
Posted: October 24, 2007
MathSciNet review: 2358484
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Abstract | References | Similar articles | Additional information

Abstract: In this article we prove the existence of a non-trivial torsion of the $ 3$-ramified Iwasawa mocule over the $ \mathbb{Z}_3^2$-extension of an imaginary quadratic field.


References:

1.
A. Bandini, Greenberg's conjecture for $ \mathbb{Z}_p^d$-extensions, Acta Arith. 108 (2003), 357-368. MR 1979904 (2004c:11201)

2.
H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields, Bull. London Math. Soc. 1 (1969), 345-348. MR 0254010 (40:7223)

3.
H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields. II, Proc. Roy. Soc. London Ser. A 322 (1971), 1551, 405-420. MR 0491593 (58:10816)

4.
S. Fujii, The torsion of $ p$-ramified Iwasawa modules, submitted.

5.
R. Greenberg, On the structure of certain Galois groups, Invent. Math. 47 (1978), 85-99. MR 504453 (80b:12007)

6.
R. Greenberg, Iwasawa theory--past and present, Class field theory--its centenary and prospect (Tokyo, 1998), 335-385, Adv. Stud. Pure Math., 30, Math. Soc. Japan, Tokyo, 2001. MR 1846466 (2002f:11152)

7.
K. Horie and J. Nakagawa, Elliptic curves with no rational points, Proc. Amer. Math. Soc. 104 (1988), 20-24. MR 958035 (89k:11113)

8.
Y. Ihara, Profinite braid groups, Galois representations and complex multiplications, Ann. Math. 123 (1986), 43-106. MR 825839 (87c:11055)

9.
T. Itoh, Pseudo-null Iwasawa modules for $ \mathbb{Z}_2^2$-extensions, submitted for publication.

10.
U. Jannsen, Iwasawa modules up to isomorphism, Algebraic number theory, 171-207, Adv. Stud. Pure Math., 17, Academic Press, Boston, MA, 1989. MR 1097615 (93c:11095)

11.
A. Lannuzel and T. Nguyen Quang Do, Conjectures de Greenberg et extensions pro-$ p$-libres d'un corps de nombres, Manuscripta Math. 102 (2000), 187-209. MR 1771439 (2001e:11106)

12.
J. Minardi, Iwasawa modules for $ \Z_p^d$-extensions of algebraic number fields, Thesis (1986), Washington University.

13.
A. Movahhedi, Sur les $ p$-extensions des corps $ p$-rationneles, Math. Nachr. 149 (1990), 163-176. MR 1124802 (92j:11131)

14.
J. Neukirch, A. Schmidt and K. Wingberg, Cohomology of number fields, Grundlehren der Mathematischen Wissenschaften, 323, Springer-Verlag, Berlin, 2000. MR 1737196 (2000j:11168)

15.
T. Nguyen Quang Do, Formations de classes et modules d'Iwasawa, Lecture Notes in Math., 1068, Springer, Berlin, 1984, 167-185. MR 756093 (85j:11156)

16.
H. Taya, Iwasawa invariants and class numbers of quadratic fields for the prime $ 3$, Proc. Amer. Math. Soc. 128 (2000), 1285-1292. MR 1641133 (2000j:11162)

17.
L. C. Washington, Introduction to cyclotomic fields. Second edition, Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1997. MR 1421575 (97h:11130)


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Additional Information:

Satoshi Fujii
Affiliation: Department of Mathematical Sciences, Graduate School of Science and Engineering, Keio University, Hiyoshi, Kohoku-ku, Yokohama City, Kanagawa, 223-8522, Japan
Email: moph@a2.keio.jp

DOI: 10.1090/S0002-9939-07-09029-6
PII: S 0002-9939(07)09029-6
Received by editor(s): August 9, 2006
Received by editor(s) in revised form: December 7, 2006
Posted: October 24, 2007
Communicated by: Ken Ono
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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