论文标题
在模块化曲线的完整共同体II的局部分析载体上II
On locally analytic vectors of the completed cohomology of modular curves II
论文作者
论文摘要
这是我们以前在模块化曲线的共同研究的本地分析向量上的延续。我们在“全态”和“抗塑形”方向上的模块化曲线上构造了差异算子。作为应用程序，我们谴责Emerton的经典性结果，该结果说，每个绝对不可还原的二维Galois表示，在P处是常规的DE RHAM，并且出现在模块化曲线的完整共同体中，都来自特征形式。此外，我们给出了$ \ mathrm {gl} _2（\ Mathbb {q} _p）$ $ \ mathrm {gl}的本地分析表示的几何描述。
This is a continuation of our previous work on the locally analytic vectors of the completed cohomology of modular curves. We construct differential operators on modular curves with infinite level at p in both "holomorphic" and "anti-holomorphic" directions. As applications, we reprove a classicality result of Emerton which says that every absolutely irreducible two dimensional Galois representation which is regular de Rham at p and appears in the completed cohomology of modular curves comes from an eigenform. Moreover we give a geometric description of the locally analytic representations of $\mathrm{GL}_2(\mathbb{Q}_p)$ attached to such a Galois representation in the completed cohomology.
