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Winter 2010 Selmer varieties for curves with CM Jacobians
John Coates, Minhyong Kim
Kyoto J. Math. 50(4): 827-852 (Winter 2010). DOI: 10.1215/0023608X-2010-015

Abstract

We study the Selmer variety associated to a canonical quotient of the Qp-pro-unipotent fundamental group of a smooth projective curve of genus at least two defined over Q whose Jacobian decomposes into a product of abelian varieties with complex multiplication. Elementary multivariable Iwasawa theory is used to prove bounds for the dimension of the Selmer variety, which, in turn, leads to a new proof of finiteness of rational points on such curves.

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John Coates. Minhyong Kim. "Selmer varieties for curves with CM Jacobians." Kyoto J. Math. 50 (4) 827 - 852, Winter 2010. https://doi.org/10.1215/0023608X-2010-015

Information

Published: Winter 2010
First available in Project Euclid: 29 November 2010

zbMATH: 1283.11092
MathSciNet: MR2740695
Digital Object Identifier: 10.1215/0023608X-2010-015

Subjects:
Primary: 11G15 , 11G30 , 11R23

Rights: Copyright © 2010 Kyoto University

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Vol.50 • No. 4 • Winter 2010
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