The de Rham functor for logarithmic D-modules
| Autor: | Clemens Koppensteiner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Functor Logarithm Holonomic General Mathematics 010102 general mathematics Duality (mathematics) General Physics and Astronomy Space (mathematics) 01 natural sciences Mathematics::Algebraic Topology Mathematics - Algebraic Geometry Morphism Mathematics::Algebraic Geometry Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences Pushforward (differential) FOS: Mathematics 010307 mathematical physics Finitely-generated abelian group 0101 mathematics Mathematics::Representation Theory Algebraic Geometry (math.AG) Mathematics |
| Popis: | 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 Poincar\'e-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. Comment: 37 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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