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arXiv · 0810.3354

Selmer varieties for curves with CM Jacobians

John Coates·Minhyong Kim
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Abstract

We study the Selmer variety associated to a canonical quotient of the $\Q_p$-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 multi-variable Iwasawa theory is used to prove dimension bounds, which, in turn, lead to a new proof of Diophantine finiteness over $\Q$ for such curves.

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John Coates, Minhyong Kim. 2008-10-18. Selmer varieties for curves with CM Jacobians. https://doi.org/10.1215/0023608x-2010-015

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