In the first part we deepen the six-functor theory of (holonomic) logarithmic D-modules, in particular with respect to duality and pushforward along projective morphisms. Then, inspired by work of Ogus, we define a logarithmic analogue of the de Rham functor, sending logarithmic D-modules to certain graded sheaves on the so-called Kato–Nakayama space. For holonomic modules we show that the associated sheaves have finitely generated stalks and that the de Rham functor intertwines duality for D-modules with a version of Poincaré–Verdier duality on the Kato–Nakayama space. Finally, we explain how the grading on the Kato–Nakayama space is related to the classical Kashiwara–Malgrange V-filtration for holonomic D-modules.

中文翻译：

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对数D模块的de Rham函子

在第一部分中，我们加深了（完整的）对数D-模的六功能理论，尤其是关于对偶性和沿射射射影射影的推论。然后，在Ogus的启发下，我们定义了de Rham函子的对数类似物，将对数D-模块发送到所谓的加藤-中山空间上的某些渐变滑轮上。对于完整的模块，我们证明了相关的滑轮具有有限的茎杆，并且de Rham函子在加藤-中山空间上将D-模块的对偶性与Poincaré-Verdier对偶性交织在一起。最后，我们解释了加藤-中山空间上的等级与完整D模块的经典Kashiwara-Malgrange V过滤如何相关。