论文标题
$ \ mathbf {z} _p^2 $ - extensions of $ \ mathbf {z}上的超高abelian品种的功能方程式
Functional equations for supersingular abelian varieties over $\mathbf{Z}_p^2$-extensions
论文作者
论文摘要
令$ k $是一个虚构的二次字段，$ k_ \ infty $是$ \ mathbf {z} _p^2 $ - $ k $的extension。回答艾哈迈德（Ahmed）和林（Lim）的问题，我们表明，塞尔默（Selmer）组的串联二重双二极管与超高极化的阿贝尔（Abelian）品种相关联，该方程式是代数功能方程。该证明使用莱，朗吉，谭和Trihan开发的$γ$系统的理论。我们还显示了代数函数方程的沿$ k_ \ infty $的Sprung的Sprung Selmer selmer组。
Let $K$ be an imaginary quadratic field and $K_\infty$ be the $\mathbf{Z}_p^2$-extension of $K$. Answering a question of Ahmed and Lim, we show that the Pontryagin dual of the Selmer group associated to a supersingular polarized abelian variety admits an algebraic functional equation. The proof uses the theory of $Γ$-system developed by Lai, Longhi, Tan and Trihan. We also show the algebraic functional equation holds for Sprung's chromatic Selmer groups of supersingular elliptic curves along $K_\infty$.
