论文标题
$ p $ adic langlands出现的结晶表示的刚性分析向量
Rigid analytic vectors of crystalline representations arising in $p$-adic Langlands
论文作者
论文摘要
令$ \ mathbf {b}（v）$为可允许的统一$ gl_2（\ mathbb {q} _p）$ - 与Breuil构建的$ p $ p $ dic-adic langlands相关的表示与二维结晶的galois表示相关的表示。 Berger和Breuil猜想了本地分析矢量的明确描述$ \ Mathbf {b}（v）_ {\ Mathrm {la}} $ of $ \ mathbf {b}（b}（v）$，该$现在由liu证明。 Emerton最近从刚性分析几何形状的角度研究了$ p $ -ADIC表示。在本文中，我们考虑了$ gl（2）$的某些刚性分析子组，并在$ \ mathbf {b}（v）_ {\ mathrm {la}} $中对刚性分析向量进行明确描述。特别是，我们显示了$ \ mathbf {b}（v）_ {\ mathrm {la}} $内部的刚性分析向量的存在，并证明了其非编号。这为我们提供了位于本地分析表示形式内部$ \ Mathbf {b}（v）_ {\ Mathrm {la}} $内部的刚性分析表示（从Emerton的意义上）。
Let $\mathbf{B}(V)$ be the admissible unitary $GL_2(\mathbb{Q}_p)$-representation associated to two dimensional crystalline Galois representation $V$ by $p$-adic Langlands constructed by Breuil. Berger and Breuil conjectured an explicit description of the locally analytic vectors $\mathbf{B}(V)_{\mathrm{la}}$ of $\mathbf{B}(V)$ which is now proved by Liu. Emerton recently studied $p$-adic representations from the viewpoint of rigid analytic geometry. In this article, we consider certain rigid analytic subgroups of $GL(2)$ and give an explicit description of the rigid analytic vectors in $\mathbf{B}(V)_{\mathrm{la}}$. In particular, we show the existence of rigid analytic vectors inside $\mathbf{B}(V)_{\mathrm{la}}$ and prove that its non-null. This gives us a rigid analytic representation (in the sense of Emerton) lying inside the locally analytic representation $\mathbf{B}(V)_{\mathrm{la}}$.
