论文标题
a $ p $ - adic的伴随$ l $ - 功能和希尔伯特模块化特征性的后果
A $p$-adic adjoint $L$-function and the ramification locus of the Hilbert modular eigenvariety
论文作者
论文摘要
让$ f $是一个完全真实的领域，$ \ mathscr {e} $由Bergdall-Hansen构建的Hilbert模块化表格的中级特征。我们研究了$ \ mathscr {e} $的分支基因座，与$ p $ - ad的属性$ l $ values的属性有关。两者之间的连接是通过分析性扭曲的Poincaré配对在crodinoid重量上进行的，该配对将希尔伯特模块化形式的经典扭曲的庞加莱配对插值，本身已知与Ghate和Dimitrov的作品相关。将配对与拉克化连接的总体策略是基于$ l $ - 理想的理论，在$ f = \ mathbb {q} $的情况下，Bellaïche和Kim使用了。
Let $F$ be a totally real field and $\mathscr{E}$ the middle-degree eigenvariety for Hilbert modular forms over $F$, constructed by Bergdall--Hansen. We study the ramification locus of $\mathscr{E}$ in relation to the $p$-adic properties of adjoint $L$-values. The connection between the two is made via an analytic twisted Poincaré pairing over affinoid weights, which interpolates the classical twisted Poincaré pairing for Hilbert modular forms, itself known to be related to adjoint $L$-values by works of Ghate and Dimitrov. The overall strategy connecting the pairings to ramification is based on the theory of $L$-ideals, which was used by Bellaïche and Kim in the case where $F = \mathbb{Q}$.
