Functorial properties of the microsupport and regularity for ind-sheaves

• DOI: 10.1007/s00209-007-0287-0
• Publication Date: 2008-03-22T13:07:27Z
• Authors: Ana Rita Martins
• Keywords: Coherent sheaf; Sheaf; Manifold (fluid mechanics)

The notion of microsupport and regularity for ind-sheaves was introduced by M. Kashiwara and P. Schapira in "Microlocal study of ind-sheaves I: microsupport and regularity". In this paper we study the behaviour of the microsupport under several functorial operations and characterize "microlocally" the ind-sheaves that are regular along involutive manifolds. As an application we prove that if a coherent D-module M is regular along an involutive manifold V (in the sense of "Systems of differential equations with regular singularities and their boundary value problems") then the ind-sheaf of temperate holomorphic solutions of M is regular along V. Another application is the notion of microsupport for sheaves on the subanalytic site, which can be given directly, without using the more complicated language of ind-sheaves.