Selmer varieties for curves with CM Jacobians
- 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.
- Publication status:
- Peer review status:
- Peer reviewed
(Accepted manuscript, pdf, 252.7KB)
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- Copyright holder:
- Kyoto University
- Copyright date:
- Copyright © 2010 Kyoto University.