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 Zp-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 weight at least 4 and level Γ0(N) with p ∤ N.
On bloch–kato selmer groups and iwasawa theory of p-adic galois representations
Longo M.;Vigni S.
2021
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 Zp-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 weight at least 4 and level Γ0(N) with p ∤ N.
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