Non-linear microlocal cut-off functors
Symplectic Geometry
2025-01-20 v2 Algebraic Geometry
Algebraic Topology
Category Theory
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 K\"unneth formulas and a functor classification result for categories of sheaves with microsupport conditions.
Cite
@article{arxiv.2406.02725,
title = {Non-linear microlocal cut-off functors},
author = {Bingyu Zhang},
journal= {arXiv preprint arXiv:2406.02725},
year = {2025}
}
Comments
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