论文标题
关于模块化曲线的完整共同体的本地分析向量
On locally analytic vectors of the completed cohomology of modular curves
论文作者
论文摘要
我们研究了模块化曲线完整的共同体学中的本地分析矢量，并确定$ \ mathfrak {gl} _2 _2（\ Mathbb {q} _p）$的理性borel子代理的特征向量。作为应用，我们证明了重量过度的特征形式的经典结果，并在某些轻度假设下为不规则案例提供了Fontaine-Mazur猜想的新证明。对于权重$ K $的过度转化特征形式，我们显示其相应的Galois表示形式具有Hodge-Tate-sen重量$ 0，K-1 $，并证明是相反的结果。
We study the locally analytic vectors in the completed cohomology of modular curves and determine the eigenvectors of a rational Borel subalgebra of $\mathfrak{gl}_2(\mathbb{Q}_p)$. As applications, we prove a classicality result for overconvergent eigenforms of weight one and give a new proof of the Fontaine-Mazur conjecture in the irregular case under some mild hypotheses. For an overconvergent eigenform of weight $k$, we show its corresponding Galois representation has Hodge-Tate-Sen weights $0,k-1$ and prove a converse result.
