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 \(\Gamma_0(N)\) with \(p\nmid N\).