In a beautiful paper, Deligne and Illusie (Invent Math 89(2):247–270, 1987) proved the degeneration of the Hodge-to-de Rham spectral sequence using positive characteristic methods. Kato (in: Igusa (ed) ALG analysis, geographic and numbers theory, Johns Hopkins University Press, Baltimore, 1989) generalized this result to logarithmic schemes. In this paper, we use the theory of twisted derived intersections developed in Arinkin et al. (Algebraic Geom 4:394–423, 2017) and the author of this paper to give a new, geometric interpretation of the Hodge theorem for the logarithmic de Rham complex.

中文翻译：

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通过导出的交点求对数de Rham复数的Hodge定理

Deligne and Illusie（Invent Math 89（2）：247-270，1987）在一篇漂亮的论文中使用正特性方法证明了Hodge-to-de Rham光谱序列的退化。加藤（在：Igusa（ed）ALG分析，地理和数字理论中，约翰·霍普金斯大学出版社，巴尔的摩，1989年）将此结果概括为对数方案。在本文中，我们使用Arinkin等人开发的扭曲派生相交理论。（Algebraic Geom 4：394–423，2017）和本文的作者对对数de Rham复数的Hodge定理给出了新的几何解释。