论文标题
关于Sharifi的猜想：特殊情况
On Sharifi's conjecture: exceptional case
论文作者
论文摘要
在本文中，我们研究了Sharifi对地图$ \varpi_θ$的溢流性的猜想。在这里，$θ$甚至是指挥$ np $的原始特征，从OHTA的意义上讲是异常的。在本地定位之后，iWasawa代数的Prime理想$ \ mathfrak {p} $与Kubota \ textendendash leopoldt $ p $ -p $ -adic $ l $ -function $ l_p（s，s，θ^{ - 1}ω^2）$，我们计算图像的图像$ \ varpi_ {θ，\ mathfrak {p}} $在本地的Galois同胞组中，并证明它是同构。另外，我们证明与模块化曲线的共同体相关的残留GALOIS表示在进行相同的定位后可以分解。
In the present article, we study the conjecture of Sharifi on the surjectivity of the map $\varpi_θ$. Here $θ$ is a primitive even Dirichlet character of conductor $Np$, which is exceptional in the sense of Ohta. After localizing at the prime ideal $\mathfrak{p}$ of the Iwasawa algebra related to the trivial zero of the Kubota\textendash Leopoldt $p$-adic $L$-function $L_p(s,θ^{-1}ω^2)$, we compute the image of $\varpi_{θ,\mathfrak{p}}$ in a local Galois cohomology group and prove that it is an isomorphism. Also, we prove that the residual Galois representations associated to the cohomology of modular curves are decomposable after taking the same localization.
