Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Kamienny's criterion and the method of Coleman and Chabauty

Author(s): Matthew H. Baker
Journal: Proc. Amer. Math. Soc. 127 (1999), 2851-2856.
MSC (1991): Primary 14G25, 11G05; Secondary 11G30
Posted: June 17, 1999
MathSciNet review: 1641625
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: This paper gives a new proof of Kamienny's Criterion using the method of Coleman and Chabauty.

References:

1.: R. Coleman: Torsion Points on Curves and $p$ -adic Abelian Integrals. Annals of Mathematics. 121, 111-168 (1985) MR 86j:14014
2.: R. Coleman: Effective Chabauty. Duke Math. J. 52, 765-770 (1985) MR 87f:11043
3.: B. Edixhoven: Rational Torsion Points on Elliptic Curves Over Number Fields [after Kamienny and Mazur]. Séminaire Bourbaki 46ème année, 1993-94, n. 782. MR 96c:11056
4.: L. Gerritzen and M. van der Put: Schottky Groups and Mumford Curves, Lecture Notes in Mathematics 817, Springer-Verlag, 1980. MR 82j:10053
5.: S. Kamienny: Torsion Points on Elliptic Curves over Fields of Higher Degree. International Mathematics Research Notices. 6, 129-133 (1992) MR 93e:11072
6.: B. Mazur: Rational Isogenies of Prime Degree. Inventiones math. 44, 129-162 (1978) MR 80h:14022
7.: W. McCallum: On the Method of Coleman and Chabauty. Mathematische Annalen. 299, 565-596 (1994) MR 95c:11079
8.: L. Merel: Bornes Pour la Torsion des Courbes Elliptiques sur les Corps de Nombres. Inventiones math. 124, 437-449 (1996) MR 96i:11057
9.: J.S. Milne: ``Abelian Varieties'' in Arithmetic Geometry (ed. Cornell, Silverman), Springer-Verlag, 1986. MR 89b:14029

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 14G25, 11G05, 11G30

Retrieve articles in all Journals with MSC (1991): 14G25, 11G05, 11G30

Additional Information:

Matthew H. Baker
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: baker@math.berkeley.edu

DOI: 10.1090/S0002-9939-99-05125-4
PII: S 0002-9939(99)05125-4
Keywords: Arithmetic geometry, modular curves, $p$-adic analysis, elliptic curves
Received by editor(s): January 7, 1998
Posted: June 17, 1999
Additional Notes: Special thanks to Loic Merel for his assistance with this work. The author of this work was supported by an NDSEG Fellowship.
Communicated by: David E. Rohrlich
Copyright of article: Copyright 1999, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|