Selmer varieties for curves with CM Jacobians
Number Theory
2015-01-14 v1 Algebraic Geometry
Abstract
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 multi-variable Iwasawa theory is used to prove dimension bounds, which, in turn, lead to a new proof of Diophantine finiteness over for such curves.
Cite
@article{arxiv.0810.3354,
title = {Selmer varieties for curves with CM Jacobians},
author = {John Coates and Minhyong Kim},
journal= {arXiv preprint arXiv:0810.3354},
year = {2015}
}