We study the Selmer variety associated to a canonical quotient of the -pro-unipotent fundamental group of a smooth projective curve of genus at least two defined over 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.
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