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On finite  -submodules of Selmer groups of elliptic curves
Author(s):
Yoshitaka
Hachimori;
Kazuo
Matsuno
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2539-2541.
MSC (2000):
Primary 11R23, 11G05
Posted:
March 1, 2000
MathSciNet review:
1690989
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Abstract:
In this note, we give another proof of a result of R. Greenberg on the non-existence of non-trivial finite  -submodules of Selmer groups.
References:
- 1.
- M. Flach, A generalisation of the Cassels-Tate pairing, J. Reine Angew. Math. 412 (1990), 113-127.MR 92b:11037
- 2.
- R. Greenberg, Iwasawa theory for
 -adic representations, in Algebraic Number Theory; Adv. Std. in Pure Math. 17 (1989), 97-137.MR 92c:11116 - 3.
- R. Greenberg, Iwasawa theory for elliptic curves, preprint, 1998.
- 4.
- L. Guo, On a generalization of Tate dualities with application to Iwasawa theory, Compositio Math. 85 (1993), 125-161. MR 94d:11085
- 5.
- J. Manin, Cyclotomic fields and modular curves, Russian Math. Surveys 26 (1971), 7-78.MR 53:5480
- 6.
- J. S. Milne, Arithmetic duality theorems, Academic Press, 1986.MR 88e:14028
- 7.
- L. C. Washington, Introduction to cyclotomic fields (2nd ed.), Graduate Texts in Math. 83, Springer-Verlag, 1997. MR 97h:11130
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Additional Information:
Yoshitaka
Hachimori
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo, 153-8914, Japan
Email:
yhachi@ms.u-tokyo.ac.jp
Kazuo
Matsuno
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo, 153-8914, Japan
Email:
matsuno@ms.u-tokyo.ac.jp
DOI:
10.1090/S0002-9939-00-05452-6
PII:
S 0002-9939(00)05452-6
Received by editor(s):
October 15, 1998
Posted:
March 1, 2000
Additional Notes:
The second author was supported by JSPS Research Fellowships for Young Scientists.
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2000,
American Mathematical Society
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