Interpolation of Generalized Heegner Cycles in Coleman Families

四元数Coleman族上广义Heegner类的插值

Interpolation of generalized Heegner classes along quaternionic Coleman families

本文通过插值构造广义Heegner类，基于Jetchev-Loffler-Zerbes的方法，在四元数模形式的Coleman族上进行研究。

Heegner points in Coleman families

We construct two-parameter analytic families of Galois cohomology classes interpolating the etale Abel--Jacobi images of generalised Heegner cycles, with both the modular form and Grossencharacter varying in p-adic families.

Beilinson-Kato和Beilinson-Flach元，Coleman-Rubin-Stark类，Heegner点和Perrin-Riou猜想

Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and the Perrin-Riou Conjecture

本文的第一个目的是解释关于Beilinson-Kato类的非平凡性的Perrin-Riou猜想的一个弱形式作为Iwasawa主定理的一个简单推论，并从这个事实和各种Gross-Zagier公式推导出它在超奇异情况下的改进版本。我们的第二个目标是建立一个概念框架的背景下，$Λ$ -adic Kolyvagin系统治疗类似物的Perrin-Riou的更高的动机，更高的排名。我们应用这个一般性的讨论，以建立一个链接Heegner点的一般类CM阿贝尔簇和（自然）科尔曼-鲁宾-斯塔克元素，我们在这里介绍。这是Rubin关于CM椭圆曲线上有理点的结果的一个高维版本。

Generalized Heegner cycles on Mumford curves

We study generalised Heegner cycles, originally introduced by Bertolini-Darmon-Prasanna for modular curves, in the context of Mumford curves. The main result of this paper relates generalized Heegner cycles with the two variable anticyclotomic $p$-adic $L$-function attached to a Coleman family $f_\infty$ and an imaginary quadratic field $K$. Our generalised Heegner cycles allow us to study the restriction of this function to non-central critical lines. The main result expresses the derivative along the weight variable of this anticyclotomic $p$-adic $L$-function restricted to non necessarily c…

四元数族的海内格点与 $p$-adic $L$-函数

Quaternionic families of Heegner points and $p$-adic $L$-functions

本文扩展了Castella的工作，研究四元数设定下的大海内格点插值与特化，并证明了四元数设定下大$p$-adic $L$-函数与大海内格点之间的显式互易律。

全实域上的四元数大Heegner点

Quaternionic big Heegner points over totally real fields

本研究将Howard的相容Heegner点族构造推广到全实域上的Gross曲线与志村曲线塔，同时处理全定与不定四元数代数，定义平行权希尔伯特模形式族的大Heegner点，构建对应p进L函数类似物与大Heegner类系统。