二维晶体表示归约的局部恒定性

Pub Date : 2020-05-03 DOI:10.5802/jtnb.1205
Emiliano Torti
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引用次数: 0

摘要

我们证明了在二维不可约晶体表示的一般素数幂集中,约化的局部恒定现象的存在。直到扭曲,这些表示取决于两个参数:轨迹$a_p$和权重$k$。使用Fontaine的$(\varphi,\Gamma)$-模理论及其由Berger via Wach模及其连续性性质引起的结晶精化,我们发现了关于$a_p$的(显式)局部恒定性结果。关于$k$(对于$a_p\not=0$)的局部恒定性结果将来自对Colmez刚性分析空间参数化三角线表示的局部研究。这项工作推广了Berger在半简单残差情况下得到的一些结果。
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Local constancy for reductions of two-dimensional crystalline representations
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 $(\varphi, \Gamma)$-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.
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