Microdifferential systems and the codimension-three conjecture

Abstract

In this paper we give a proof of a fundamental conjecture, the codi-mension-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 sup-port. 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. © 2014 Department of Mathematics, Princeton University.