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arXiv · 1712.09085

Euler systems for Galois deformations and the pseudo-isomorphism class of the dual of fine Selmer groups

Tatsuya Ohshita
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Abstract

In this article, we study the pseudo-isomorphism class of the dual fine Selmer group $X$ attached to a $p$-adic Galois deformation whose deformation ring $\Lambda$ is isomorphic to the ring of formal power series. By using the "Kolyvagin system" arising from a given Euler system $c$, we shall construct ideals $C_i(c)$ of $\Lambda$, and prove that the ideals $C_i(c)$ approximate the higher Fitting ideals of $X$ under suitable hypothesis. In particular, we shall prove that the ideals $C_i(c)$ arising from the Euler system of Beilinson-Kato elements determine the pseudo-isomorphism classes of the dual fine Selmer groups attached to ordinary and nearly ordinary Hida deformations satisfying certain conditions.

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Tatsuya Ohshita. 2017-12-25. Euler systems for Galois deformations and the pseudo-isomorphism class of the dual of fine Selmer groups. https://arxiv.org/abs/1712.09085

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