论文标题
离散环的ADIC空间上的对数差异
Logarithmic differentials on discretely ringed adic spaces
论文作者
论文摘要
在平稳的离散响起的ADIC空间$ \ MATHCAL {X} $上的字段$ k $上，我们定义了一个差速器$ω_ {\ Mathcal {\ Mathcal {x}} $的sheaf $ω_ {\ Mathcal {\ Mathcal {x}}}^+$。它的定义与$ \ Mathcal {O}的$ \ Mathcal {X}} $ of $ \ MATHCAL {O} _ {\ MATHCAL {X}} $使用Kähhlerseminorms on $ {我们在对数差异方面给出了$ω^+_ {\ Mathcal {x}} $的描述。如果$ \ mathcal {x} $是$ \ mathrm {spa}（x，x，x，\ bar {x}）$ for Schemion $ \ bar {x} $和一个开放的子cheme $ x $，以使$ \ bar {x} $上的相应日志结构很顺利，我们显示$ω^+_ {\ Mathcal {x}}（\ Mathcal {x}）$是$（x，x，\ bar {x}）$的对数差异的同构。
On a smooth discretely ringed adic space $\mathcal{X}$ over a field $k$ we define a subsheaf $Ω_{\mathcal{X}}^+$ of the sheaf of differentials $Ω_{\mathcal{X}}$. It is defined in a similar way as the subsheaf $\mathcal{O}^+_{\mathcal{X}}$ of $\mathcal{O}_{\mathcal{X}}$ using Kähler seminorms on $Ω_{\mathcal{X}}$. We give a description of $Ω^+_{\mathcal{X}}$ in terms of logarithmic differentials. If $\mathcal{X}$ is of the form $\mathrm{Spa}(X,\bar{X})$ for a scheme $\bar{X}$ and an open subscheme $X$ such that the corresponding log structure on $\bar{X}$ is smooth, we show that $Ω^+_{\mathcal{X}}(\mathcal{X})$ is isomorphic to the logarithmic differentials of $(X,\bar{X})$.
