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arXiv · 2608.25309

Pseudonullity for fine Selmer groups over multiple $\mathbb{Z}_p^{d}$-extensions

Peikai Qi·Ruichen Xu
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Abstract

In this article, we develop vertical control theorems for fine Selmer groups associated with Galois representations and their deformations in $p$-adic families. We apply them to provide new evidence for Conjectures A and B of Coates--Sujatha and to obtain pseudonullity of the fine Selmer groups for cyclotomic characters, elliptic curves, classical cuspidal newforms, and Hida families of $p$-ordinary cuspidal newforms.

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Peikai Qi, Ruichen Xu. 2026-08-26. Pseudonullity for fine Selmer groups over multiple $\mathbb{Z}_p^{d}$-extensions. https://arxiv.org/abs/2608.25309

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