Microlocal study of ind-sheaves I: micro-support and regularity

We define the notions of micro-support and regularity for ind-sheaves, and prove their invariance by contact transformations. We apply the results to the ind-sheaves of temperate holomorphic solutions of D-modules. We prove that the micro-support of such an ind-sheaf is the characteristic variety of the corresponding D-module and that the ind-sheaf is regular if the D-module is regular holonomic.