Non-linear microlocal cut-off functors

Abstract

To any conic closed set of a cotangent bundle, one can associate four functors on the category of sheaves, which are called non-linear microlocal cut-off functors. Here we explain their relation with the microlocal cut-off functor defined by Kashiwara and Schapira, and prove a microlocal cut-off lemma for non-linear microlocal cut-off functors, adapting inputs from symplectic geometry. We also prove two Künneth formulas and a functor classification result for categories of sheaves with microsupport conditions.

v2: 17 pages. Final version to appear in Rend. Sem. Mat. Univ. Padova. Some discussion on the Omega-lens definition of microsupport and requirement on the coefficient are added