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

Matteo Longo; Stefano Vigni

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arXiv · 2010.10251

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

Matteo Longo·Stefano Vigni

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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 $p\nmid N$.

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Matteo Longo, Stefano Vigni. 2020-10-20. On Bloch-Kato Selmer groups and Iwasawa theory of $p$-adic Galois representations. https://arxiv.org/abs/2010.10251

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