论文标题
精细的模块化形式组
Fine Selmer groups of modular forms
论文作者
论文摘要
我们将$ p $ - 阿迪·加洛伊斯（Galois）代表的优质selmer群体与可接受的$ p $ $ p $ - 亚种式的谎言扩展与沿这些谎言延伸的理想班级组的伊瓦萨瓦不变性相比。 更确切地说，让$ k $为一个数字字段，让$ v $为$ p $ ad的代表$ k $ $ k $的$ g_k $ g_k $，然后选择$ g_k $ -invariant lattice $ {t \ subseteq v} $。我们研究了$ {a = v/t} $的精细selmer群体，上面是$ p $ p $ -Adic lie扩展$ k_ \ infty/k $，将其Corank和$μ$ invariant与Corank和$μ$ $ $ $ $ invariant进行比较，以及$ K_ \ infty/k $的理想级别组的iWasawa Invariant。 在本文的第二部分中，我们一方面比较了iWasawa $μ$ - 和$ l_0 $ -invariants，一方面是CM模块化表单的精美Selmer组，另一方面比较了理想班级组的iWasawa docliants，另一方面，iWasawa of the Inderainds of Mather of Mathbb {Z} _p $ extensenions to triavialization of Broce of tocce。
We compare the Iwasawa invariants of fine Selmer groups of $p$-adic Galois representations over admissible $p$-adic Lie extensions of a number field $K$ to the Iwasawa invariants of ideal class groups along these Lie extensions. More precisely, let $K$ be a number field, let $V$ be a $p$-adic representation of the absolute Galois group $G_K$ of $K$, and choose a $G_K$-invariant lattice ${T \subseteq V}$. We study the fine Selmer groups of ${A = V/T}$ over suitable $p$-adic Lie extensions $K_\infty/K$, comparing their corank and $μ$-invariant to the corank and the $μ$-invariant of the Iwasawa module of ideal class groups in $K_\infty/K$. In the second part of the article, we compare the Iwasawa $μ$- and $l_0$-invariants of the fine Selmer groups of CM modular forms on the one hand and the Iwasawa invariants of ideal class groups on the other hand over trivialising multiple $\mathbb{Z}_p$-extensions of $K$.
