Notes on the local p-adic Simpson correspondence
Notes on the local p-adic Simpson correspondence
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关于本地 p-adic Simpson 通信的注释
DOI：
10.1007/s00208-018-1655-2
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发表时间：
2018
影响因子：
1.4
通讯作者：
Takeshi Tsuji
中科院分区：
文献类型：
--
作者：
朝比奈優;山田優子;吉井一倫 ;洪 鋒雷;Hirotsugu Yamamoto;Takeshi Tsuji
我们完成了理论的局部进辛普森对应开发的法尔亭合理的系数。证明了在具有理想剩余域的混合特征（0，p）的完全离散赋值环上，一类对数光滑仿射方案的几何基本群的小广义表示范畴与小Higgs丛的小广义表示范畴是等价的.困难在于从前者构造后者，我们通过推广的Sen关于对数光滑仿射格式的理论给出了后者，该理论依赖于Faltings的几乎纯性定理。受R. Liu和X. Zhu最近工作的启发，我们还给出了算术基本群的-广义表示的局部进Simpson对应的一个公式，以及Hodge-Tate广义表示的一个刻画.
We complete the theory of the localp-adic Simpson correspondence developed by Faltings for rational coefficients. It asserts that there is an equivalence between the category of small-generalized representations of the geometric fundamental group and that of small-Higgs bundles for a certain kind of log smooth affine scheme over a complete discrete valuation ring of mixed characteristic (0,p) with perfect residue field. The difficulty lies in the construction of the latter from the former, and we give it via a generalized Sen’s theory for the log smooth affine scheme, which depends on Faltings’ almost purity theorem. Inspired by a recent work by R. Liu and X. Zhu, we also give a formulation of localp-adic Simpson correspondence for-generalized representations of the arithmetic fundamental group, and a characterization of Hodge-Tate generalized representations in terms of the correspondence.