论文标题
整体$ p $ -adic Hodge理论在不完美的残留场案例中
Integral $p$-adic Hodge theory in the imperfect residue field case
论文作者
论文摘要
让$ k $是一个混合特征的完整离散估值字段，残留场承认有限的$ p $ basis，让$ g_k $为Galois组。我们首先将$ g_k $的半稳定表示形式分类为具有连接的弱化过滤$（φ，n）$ - 模块。然后，我们从\ emph {intemal}的类别构建一个完全忠实的函数，$ g_k $的半稳定表示为breuil-kisin $ g_k $ -modules的类别。使用积分理论，我们将$ p $ - 可分布的群体对$ k $的整数圈进行了分类，该组由小breuil-kisin模块与连接进行了分类。
Let $K$ be a mixed characteristic complete discrete valuation field with residue field admitting a finite $p$-basis, and let $G_K$ be the Galois group. We first classify semi-stable representations of $G_K$ by weakly admissible filtered $(φ,N)$-modules with connections. We then construct a fully faithful functor from the category of \emph{integral} semi-stable representations of $G_K$ to the category of Breuil-Kisin $G_K$-modules. Using the integral theory, we classify $p$-divisible groups over the ring of integers of $K$ by minuscule Breuil-Kisin modules with connections.
