Microdifferential systems and the codimension-three conjecture


In this paper we give a proof of a fundamental conjecture, the codimension-three conjecture, for microdifferential holonomic systems. The conjecture states that any (regular) holonomic module extends uniquely beyond an analytic subset that is at least of codimension three in its support. Our result can also be interpreted from a topological point of view as a statement about microlocal perverse sheaves. However, our proof is entirely in the context of microdifferential holonomic systems.


Masaki Kashiwara

Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan and
Seoul National University, Seoul, Korea

Kari Vilonen

Northwestern University, Evanston, IL and
Helsinki University, Helsinki, Finland