New York Journal of Mathematics
Volume 27 (2021), 437-467


Matteo Longo and Stefano Vigni

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

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Published: March 5, 2021.
Keywords: Selmer groups, Iwasawa theory, p-adic Galois representations, modular forms.
Subject: 11R23, 11F80.

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.


The authors are supported by PRIN 2017 "Geometric, algebraic and analytic methods in arithmetic" and by GNSAGA--INdAM.

Author information

Matteo Longo:
Dipartimento di Matematica
Universitá di Padova
Via Trieste 63, 35121 Padova, Italy


Stefano Vigni:
Dipartimento di Matematica
Universitá di Genova
Via Dodecaneso 35, 16146 Genova, Italy