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摘要翻译：
本文研究系数为任意维数的G_K的晶体表示，其中K是A阶Q_p的未分支扩张。本文证明了当σ不变Hodge-Tate权小于p-1时Fontaine-Laffaille型定理，该定理建立了晶体表示的Galois稳定格与强可分的phi格之间的双射。在推广Breuil工作的基础上，我们对2维G_K的所有可约和不可约晶体表示进行了分类，并描述了它们的mod p约化。我们将Deligne、Fontaine-Serre和Edixhoven的一些结果推广到Hilbert模形式在不变Hodge-Tate权小于p-1时的表示。
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英文标题：
《Crystalline representations of G_Qp^a with coefficients》
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作者：
Hui June Zhu
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
This paper studies crystalline representations of G_K with coefficients of any dimension, where K is the unramified extension of Q_p of degree a. We prove a theorem of Fontaine-Laffaille type when \sigma-invariant Hodge-Tate weight less than p-1, which establishes the bijection between Galois stable lattices in crystalline representations and strongly divisible \phi-lattice. In generalizing Breuil's work, we classify all reducible and irreducible crystalline representations of G_K of dimensional 2, then describe their mod p reductions. We generalize some results (of Deligne, Fontaine-Serre, and Edixhoven) to representations arising from Hilbert modular forms when \sigma-invariant Hodge-Tate weight less than p-1.
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PDF链接：
https://arxiv.org/pdf/0807.1078
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