Given a logarithmic $1$-form on the snc locus of a log canonical surface pair $(X,D)$ over a perfect field of characteristic $p\ge 7$, we show that it extends with at worst logarithmic poles to any resolution of singularities. We also prove the analogous statement for regular differential forms, under an additional tameness hypothesis. In addition, residue and restriction sequences for tamely dlt pairs are established. We give a number of examples showing that our results are sharp in the surface case, and that they fail in higher dimensions. On the other hand, our techniques yield a new proof of the characteristic zero Logarithmic Extension Theorem in any dimension.

中文翻译：

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正特征对数规范空间的微分形式

给定一个对数$1$-在对数规范曲面对的 snc 轨迹上形成$(X,D)$在一个完美的特征场上$p\ge 7$，我们证明它在最坏的对数极点上扩展到任何奇点的分辨率。我们还在一个额外的驯服假设下证明了规则微分形式的类似陈述。此外，建立了温和的 dlt 对的残基和限制序列。我们给出了一些例子，表明我们的结果在表面情况下很清晰，但在更高维度上却失败了。另一方面，我们的技术在任何维度上产生了特征零对数扩展定理的新证明。