# Nearby cycles and specialisation - properties

I am looking for reference for properties of nearby cycles - specifically, commutation with non-characteristic pull-back (good enough - commutation with pull-back to closed subvariety which is transversal to a stratification for which our sheaf is smooth). I would like a reference for any of the following settings:

• D-modules using V-filtration or Beilinsons definition
• l-adic sheaves
• constructible sheaves in the "usual complex world"

Thank you, Sasha

## 1 Answer

For the first item, section 3 of M. Saito's Modules de Hodge Polarizables is pretty thorough. He works in the filtered $D$-module setting, but I suppose you can ignore that aspect. For the constructible setting, perhaps you can look at Dimca's Sheaves in Topology.