Selmer varieties for curves with CM Jacobians

Details Selmer varieties for curves with CM Jacobians Selmer varieties for curves with CM Jacobians

2008-10-18

arxiv.org/abs/0810.3354v1

Mathematics

Number Theory

Scientific paper

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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