On differential modules associated to de Rham representations in the imperfect residue field case
On differential modules associated to de Rham representations in the imperfect residue field case
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DOI：
10.2140/ant.2015.9.1881
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发表时间：
2013-07
影响因子：
1.3
通讯作者：
Shun Ohkubo
中科院分区：
文献类型：
--
作者：
Shun Ohkubo
设K是具有混合特征的完备离散赋值域，其剩余域不一定是完美的，G_K是K的绝对Galois群.在本文的第一部分中，我们证明了Scholl对$K$上范数域的推广与Abbes-Saito的分歧理论是相容的。在第二部分中，我们构造了一个函子$\mathbb{N}_{\mathrm{dR}}（V）$，它将一个de Rham表示$V$与一个Kedlaya意义下的$（\varphi，\nabla）$-模联系起来。最后证明了Kedlaya微分Swan导体$\mathbb{N}_{\mathrm{dR}}（V）$与Swan导体$V$的相容性，推广了马尔莫拉的公式.
Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$, whose residue field may not be perfect, and $G_K$ the absolute Galois group of $K$. In the first part of this paper, we prove that Scholl's generalization of fields of norms over $K$ is compatible with Abbes-Saito's ramification theory. In the second part, we construct a functor $\mathbb{N}_{\mathrm{dR}}(V)$ associating a de Rham representation $V$ with a $(\varphi,\nabla)$-module in the sense of Kedlaya. Finally, we prove a compatibility between Kedlaya's differential Swan conductor of $\mathbb{N}_{\mathrm{dR}}(V)$ and Swan conductor of $V$, which generalizes Marmora's formula.