In this paper, we study the growth of fine Selmer groups in two cases. First, we study the growth of fine Selmer ranks in multiple $\mathbb{Z}_{p}$ -extensions. We show that the growth of the fine Selmer group is unbounded in such towers. We recover a sufficient condition to prove the $\unicode[STIX]{x1D707}=0$ conjecture for cyclotomic $\mathbb{Z}_{p}$ -extensions. We show that in certain non-cyclotomic $\mathbb{Z}_{p}$ -towers, the $\unicode[STIX]{x1D707}$ -invariant of the fine Selmer group can be arbitrarily large. Second, we show that in an unramified $p$ -class field tower, the growth of the fine Selmer group is unbounded. This tower is non-Abelian and non- $p$ -adic analytic.

在本文中，我们研究了两种情况下优良Selmer组的增长。首先，我们研究多个 $ \ mathbb {Z} _ {p} $ -扩展名中Selmer等级的增长。我们表明，在此类塔中，优秀的Selmer集团的增长是无限的。我们恢复了充分的条件，以证明对于 环原子 $ \ mathbb {Z} _ {p} $ -扩展名的$ \ unicode [STIX] {x1D707} = 0 $ 猜想。我们表明，在某些非杂环的 $ \ mathbb {Z} _ {p} $- 塔中，精细Selmer组的 $ \ unicode [STIX] {x1D707} $-不 变量可以任意大。其次，我们表明，在未分叉的 $ p $ 级场塔中，优良的Selmer集团的增长是无限的。这个塔是非阿贝尔和非 $ p $ -adic分析。