论文标题
Iwasawa的椭圆形模块化形式的曲折理论是惰性素数的假想二次磁场
Iwasawa theory of twists of elliptic modular forms over imaginary quadratic fields at inert primes
论文作者
论文摘要
本文中我们的主要目的是研究$ \ mathrm {gl} _2 _2 \ times \ times \ mathrm {res} _ {k/\ mathbb {q}}} \ mathrm {glrm {gl} _1 $，$ k $ ity priph priph priph prime prime priph priped priped priph priph priped priped priped priped priped priped ymath prips $ quadr，在这种情况下，我们证明了对Iwasawa主要猜想的可划分结果，利用了Perrin-Riou功能的优化签名分解程序和Beilinson-Flach-Flach Elements，用于兰金伯格（Rankin）的家族 - $ p $ - 非凡形式的固定$ p $ p $ nonon-non-non-non-non-non-onon-ordar-ordornary modular form。最佳性使对Selmer群体的$ $ $ invariants和$ p $ - adic $ l $ functions的有效控制作为模块化形式各不相同，这对于我们的修补论点至关重要，在三个变量中，在iWasawa Main的猜想中建立一种划分。
Our primary goal in this article is to study the Iwasawa theory for semi-ordinary families of automorphic forms on $\mathrm{GL}_2\times\mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1$, where $K$ is an imaginary quadratic field where the prime $p$ is inert. We prove divisibility results towards Iwasawa main conjectures in this context, utilizing the optimized signed factorization procedure for Perrin-Riou functionals and Beilinson--Flach elements for a family of Rankin--Selberg products of $p$-ordinary forms with a fixed $p$-non-ordinary modular form. The optimality enables an effective control on the $μ$-invariants of Selmer groups and $p$-adic $L$-functions as the modular forms vary in families, which is crucial for our patching argument to establish one divisibility in an Iwasawa main conjecture in three variables.
