关于潜在半稳定表示的Emerton-Gee栈
On the Emerton-Gee stack of potentially semistable representations
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中文总结 AI 辅助
该研究利用Breuil-Kisin模变体分类潜在半稳定伽罗瓦表示，构建其栈并证明与Emerton-Gee栈同构，构造相关映射并证明其光滑性，得到对应全局正则性结果。
中文摘要 AI 辅助
我们首先利用Breuil-Kisin模的一些变体，对给定的驯服惯性型的潜在半稳定伽罗瓦表示进行分类。随后我们构造此类Breuil-Kisin模的若干“模型”。在此基础上，我们构建我们版本的Breuil-Kisin模构成的栈，并证明该栈同构于潜在半稳定表示的Emerton-Gee栈。这还使得我们能够构造从潜在半稳定EG栈的刚性一般纤维到Weil-Deligne表示栈的解析化的映射，该映射“插值”了Fontaine将Weil-Deligne表示关联到潜在半稳定伽罗瓦表示的方案。我们证明该映射的光滑性，并得到潜在半稳定EG栈的一般形式光滑性性质，这可视为Kisin关于相应伽罗瓦变形环的正则性结果的全局版本。
英文摘要
We first classify the potentially semistable Galois representations of a given tame inertial type using some variants of Breuil-Kisin modules. Then we construct some ``model" of such Breuil-Kisin modules. From here, we build a stack of our version of Breuil-Kisin modules, and show that it is isomorphic to the Emerton-Gee stack of potentially semistable representations. This also makes it possible to construct a map from the rigid generic fiber of the potentially semistable EG stack to the analytification of the stack of Weil-Deligne representations, which ``interpolates" Fontaine's recipe of associating Weil-Deligne representations to potentially semistable Galois representations. We prove the smoothness of this map, and obtain the generic formal smoothness property of the potentially semistable EG stack. This can be regarded as the global version of Kisin's regularity results on the corresponding Galois deformation rings.
