论文标题
$λ$ -ADIC模块的扭曲引理
Twisting lemma for $Λ$-adic modules
论文作者
论文摘要
一个经典的扭曲引理说，鉴于iWasawa代数$ \ Mathbb {z} _p [[γ] $，带有$γ\ cong \ mathbb {z} _p，_p，\ \ \ a n congrance $ time $ timal $ timate $ grow time timage $ timate $ grow，给定有限生成的扭转模块$ m $ $ m $那就是$γ^{n} $ - twist $ m（θ）$的Euler特征对于每个$ n $都是有限的。这种扭曲的引理已被概括为一般紧凑型$ p $ adic lie Group $ g $的Iwasawa代数。在本文中，我们考虑将扭曲引理对$ \ Mathcal {t} [[g]] $模块的进一步概括，其中$ g $是一个紧凑型$ P $ -ADIC LIE GROUP和$ \ MATHCAL {t} $是$ \ Mathbb {Z} _p [xp [x] $的有限扩展。这种模块自然出现在HIDA理论中。我们还通过考虑大型Selmer（分别为Fine Selmer）组的扭曲的Euler特征来指示算术应用，该特征是$λ$ - adic形式的$λ$ - adic形式。
A classical twisting lemma says that given a finitely generated torsion module $M$ over the Iwasawa algebra $\mathbb{Z}_p[[Γ]]$ with $Γ\cong \mathbb{Z}_p, \ \exists$ a continuous character $θ: Γ\rightarrow \mathbb{Z}_p^\times$ such that, the $ Γ^{n}$-Euler characteristic of the twist $M(θ)$ is finite for every $n$. This twisting lemma has been generalized for the Iwasawa algebra of a general compact $p$-adic Lie group $G$. In this article, we consider a further generalization of the twisting lemma to $\mathcal{T}[[G]]$ modules, where $G$ is a compact $p$-adic Lie group and $\mathcal{T}$ is a finite extension of $\mathbb{Z}_p[[X]]$. Such modules naturally occur in Hida theory. We also indicate arithmetic application by considering the twisted Euler Characteristic of the big Selmer (respectively fine Selmer) group of a $Λ$-adic form over a $p$-adic Lie extension.
