论文标题
二维晶体表示的局部恒定
Local constancy for reductions of two-dimensional crystalline representations
论文作者
论文摘要
我们证明了在二维不可还原晶体表示的一般主要功率设置中降低的局部恒定现象的存在。这些表示形式取决于两个参数：trace $ a_p $和权重$ k $。我们使用Fontaine的$（φ，γ）$ - 模块的理论发现了（显式的）局部恒定结果（明确的）局部恒定结果及其结晶细化，因为Berger通过WACH模块及其连续性属性。关于$ k $的本地恒定结果（对于$ a_p \ not = 0 $）将来自对科尔姆斯刚性分析空间参数化三角形表示的本地研究。这项工作扩大了在半简单残留案例中获得的Berger的一些结果。
We prove the existence of local constancy phenomena for reductions in a general prime power setting of two-dimensional irreducible crystalline representations. Up to twist, these representations depend on two parameters: a trace $a_p$ and a weight $k$. We find an (explicit) local constancy result with respect to $a_p$ using Fontaine's theory of $(φ, Γ)$-modules and its crystalline refinement due to Berger via Wach modules and their continuity properties. The local constancy result with respect to $k$ (for $a_p\not=0$) will follow from a local study of Colmez's rigid analytic space parametrizing trianguline representations. This work extends some results of Berger obtained in the semi-simple residual case.
