论文标题
Lubin-Tate理论和过度融合的希尔伯特模块化形式的低重量
Lubin-Tate theory and overconvergent Hilbert modular forms of low weight
论文作者
论文摘要
令$ k $为$ \ mathbb {q} _ {p} $的有限扩展名，让$γ$为$ k $的环形分量扩展的Galois组。 Fontaine的理论将$ \ Mathrm {gal} \ left的$ P $ -ADIC表示形式分类（\ overline {k}/k \ right）$在$（φ，γ）$ - 模块方面。此分类的一个有用方面是伯格的词典，它表达了不变的$ p $ - adge hodge理论，就这些$ \ lest（φ，γ\ right）$ - 模块而言。在本文中，我们使用本地分析矢量的理论将本字典概括为$γ$是$ k $的lubin-tate扩展的Galois组。作为一个应用程序，我们表明，如果$ f $是一个完全真实的数字字段，而$ v $是$ f $位于$ p $上方的$ f $，那么$ p $ - adic代表的$ \ mathrm {gal} \ left（\ overline {f} _ {v} _ {v}/f_}/f_ {v}/f_ {v} \ right） $ f_ {v} $ - 分析性的扭曲是lubin-tate三角形。此外，我们根据$ v $的hecke特征值确定三角剖分。这将导致Chenevier，Colmez和Kisin先前获得的情况下的情况。
Let $K$ be a finite extension of $\mathbb{Q}_{p}$ and let $Γ$ be the Galois group of the cyclotomic extension of $K$. Fontaine's theory gives a classification of $p$-adic representations of $\mathrm{Gal}\left(\overline{K}/K\right)$ in terms of $(φ,Γ)$-modules. A useful aspect of this classification is Berger's dictionary which expresses invariants coming from $p$-adic Hodge theory in terms of these $\left(φ,Γ\right)$-modules. In this paper, we use the theory of locally analytic vectors to generalize this dictionary to the setting where $Γ$ is the Galois group of a Lubin-Tate extension of $K$. As an application, we show that if $F$ is a totally real number field and $v$ is a place of $F$ lying above $p$, then the $p$-adic representation of $\mathrm{Gal}\left(\overline{F}_{v}/F_{v}\right)$ associated to a finite slope overconvergent Hilbert eigenform which is $F_{v}$-analytic up to a twist is Lubin-Tate trianguline. Furthermore, we determine a triangulation in terms of a Hecke eigenvalue at $v$. This generalizes results in the case $F=\mathbb{Q}$ obtained previously by Chenevier, Colmez and Kisin.
