AI 中文总结
本文扩展Greenberg的岩泽不变量研究框架，比较普通p进表示的Selmer群在Greenberg邻域内ℤₚ扩张上的岩泽不变量，为精细Selmer群建立类似结果，并为分圆ℤₚ扩张邻域内相关特征理想与p进L函数的联系提供证据。
AI 中文摘要
设K为数域，p为奇素数。Greenberg在K的所有ℤₚ扩张空间上引入了自然拓扑，并建立了经典岩泽不变量的若干有界性结果。我们将该框架扩展，以比较Greenberg邻域内ℤₚ扩张上附属于普通p进表示的Selmer群的岩泽不变量。我们还为精细Selmer群建立了类似结果。最后，在分圆ℤₚ扩张的邻域内，我们为Disegni引入的Selmer群特征理想与猜想p进L函数之间的预期联系提供了证据。
英文摘要
Let $K$ be a number field and $p$ be an odd prime. Greenberg introduced a natural topology on the space of all $\mathbb{Z}_p$-extensions of $K$ and established several boundedness results for the classical Iwasawa invariants. We extend this framework to compare the Iwasawa invariants of Selmer groups attached to an ordinary $p$-adic representation across $\mathbb{Z}_p$-extensions lying in a Greenberg neighbourhood in the sense of Greenberg. We also establish analogous results for the fine Selmer groups. Finally, in a neighbourhood of the cyclotomic $\mathbb{Z}_p$-extension, we provide evidence for the expected connection between the characteristic ideal of the Selmer group and the conjectural $p$-adic $L$-function introduced by Disegni.
Comments14 pages
