The de Rham functor for logarithmic D-modules

• Clemens Koppensteiner ^[1]
  1. [1] Institute for Advanced Study

     Institute for Advanced Study

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 3, 2020
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.