On Bloch-Kato Selmer groups and Iwasawa theory of $p$-adic Galois representations

Abstract

A result due to R. Greenberg gives a relation between the cardinality of Selmer groups of elliptic curves over number fields and the characteristic power series of Pontryagin duals of Selmer groups over cyclotomic ${\mathbb{Z}}_p$-extensions at good ordinary primes $p$. We extend Greenberg's result to more general $p$-adic Galois representations, including a large subclass of those attached to $p$-ordinary modular forms of level $\hat{I}{“}_0(N)$ with $p\nmid N$.

21 pages