Holonomic and perverse logarithmic D-modules
| Autor: | Mattia Talpo, Clemens Koppensteiner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Perverse t-structure
Pure mathematics D-modules Duality Logarithmic geometry Mathematics (all) Logarithm Verdier duality General Mathematics 01 natural sciences 14F10 14A99 16A49 Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences Immersion (mathematics) FOS: Mathematics Computer Science::Symbolic Computation 0101 mathematics Algebraic Geometry (math.AG) Mathematics Functor Holonomic 010102 general mathematics 010307 mathematical physics |
| Popis: | We introduce the notion of a holonomic D-module on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In contrast to the classical case, the pushforward of a holonomic module along an open immersion is in general not holonomic. We introduce a "perverse" t-structure on the category of coherent logarithmic D-modules which makes the dualizing functor t-exact on holonomic modules. This allows us to transfer some of the formalism from the classical setting and in particular show that every holonomic module on an open subscheme can be extended to a holonomic module on the whole space. Conversely this t-exactness characterizes holonomic modules among all coherent logarithmic D-modules. We also introduce logarithmic versions of the Gabber and Kashiwara-Malgrange filtrations. Comment: 30 pages |
| Databáze: | OpenAIRE |
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