Abstract:In this article we study the algebraic structure of fine Mordell--Weil groups, plus/minus Mordell--Weil groups, Selmer groups, and plus/minus Selmer groups in the cyclotomic $\mathbb{Z}_p$-extensions of abelian number fields. As a first, we prove theorems on the equivariant structure of fine Mordell--Weil groups and plus/minus Mordell--Weil groups. In other words, we study the explicit shape of the fine, plus/minus objects as a $\Lambda(\mathcal{G})$-module with $\mathcal{G} \simeq \mathbb{Z}_p \times G$ and $G$ a finite abelian group. We prove refinements of previously known results over $\mathbb{Q}$ for the classical Selmer group and the plus/minus Selmer group, and subsequently also the Shafarevich--Tate group, and the plus/minus Shafarevich--Tate group. This gives new evidence towards an affirmative answer for the Kurihara--Pollack problem.
From: Rusiru Gambheera [view email]
[v1]
Sun, 27 Jul 2025 16:14:36 UTC (27 KB)
[v2]
Thu, 25 Sep 2025 00:56:55 UTC (27 KB)
[v3]
Tue, 16 Jun 2026 17:26:55 UTC (31 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。