论文标题
控制精细的Selmer组的定理，以及附在模块化形式的精细Selmer组的双重性
Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms
论文作者
论文摘要
令$ \ mathcal {o} $为$ \ mathbb {q} _p $的有限扩展名的整数环。我们证明了两个在$ \ mathcal {o} $上获得一般生成的模块的精细Selmer组的控制定理。我们应用这些控制定理将附加到模块化表格$ f $的精细selmer组上的$ \ mathbb {z} _p $ - extension $ \ mathbb {q} $与连接的conjugate Modular Modular form $ + edline $ \ + edline {f} $的对应物。
Let $\mathcal{O}$ be the ring of integers of a finite extension of $\mathbb{Q}_p$. We prove two control theorems for fine Selmer groups of general cofinitely generated modules over $\mathcal{O}$. We apply these control theorems to compare the fine Selmer group attached to a modular form $f$ over the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ to its counterpart attached to the conjugate modular form $\overline{f}$.
