论文标题
比较一致的模块化形式的阳性核心的反风速selmer组 - 第二部分
Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms -- Part II
论文作者
论文摘要
我们研究了s_ {2r}（2r}（γ_0（n））$的SELMER组与反通风$ \ MATHBB {Z} _p $ - extension的s_ {2r}（γ_0（n））$相关联。在某些假设下，我们证明该Selmer集团没有适当的$λ$ -Submodules的有限索引。这概括了在椭圆曲线案例中Bertolini的工作。我们还提供了校正和改进对本作者一致模块化形式的早期结果的改进。
We study the Selmer group associated to a $p$-ordinary newform $f \in S_{2r}(Γ_0(N))$ over the anticyclotomic $\mathbb{Z}_p$-extension of an imaginary quadratic field $K/\mathbb{Q}$. Under certain assumptions, we prove that this Selmer group has no proper $Λ$-submodules of finite index. This generalizes work of Bertolini in the elliptic curve case. We also offer both a correction and an improvement to an earlier result on Iwasawa invariants of congruent modular forms by the present authors.
