论文标题
关于硫泽理论的几何观点
A geometric view on Iwasawa theory
论文作者
论文摘要
本文将我们对$ p $ - 亚种特征库的几何形状扩展到重量$ 1 $ cuspform $ f $不规则的$ p $且具有复杂乘法的位置，以及在伊瓦沙瓦和HIDA理论中的含义。新颖的结果包括确定属于$ f $的广义特征空间的某些非经典$ p $ p $ addic模块化形式的傅立叶系数，这是$ p $ f $的代数数字对数。我们还计算了包含$ f $的HIDA家族的$ P $ fortrations的“神秘”交叉比例。
This article extends our study of the geometry of the $p$-adic eigencurve at a point defined by a weight $1$ cuspform $f$ irregular at $p$ and having complex multiplication, and the implications in Iwasawa and in Hida theories. The novel results include the determination of the Fourier coefficients of certain non-classical $p$-adic modular forms belonging to the generalized eigenspace of $f$, in terms of $p$-adic logarithms of algebraic numbers. We also compute the "mysterious" cross-ratios of the $p$-ordinary filtrations of the Hida families containing $f$.
