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

2020/10/20 by Matteo Longo, Longo, Matteo, Stefano Vigni +1 · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2010.10251

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 Γ₀(N) with p\nmid N.

Cited by

• Partial Bloch--Kato Selmer groups of B-pairs as delta functors
• A Weight Structure on Rigid Analytic Motives over a Field
• Perfectoid Spaces in Multivariate p-adic Hodge Theory

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• Iwasawa theory for elliptic curves at supersingular primes over Z_p-extensions of number fields
• Deformations of reducible Galois representations with large Selmer p-rank