Characteristic cycles of constructible sheaves and microlocalization

Takeshi Saito

Characteristic cycles of constructible sheaves and microlocalization

Algebraic Geometry 2026-07-19 v1

Authors: Takeshi Saito

Abstract

For a constructible sheaf on a smooth scheme over a field of positive characteristic, the singular support and the characteristic cycle are defined on the cotangent bundle. We study if a construction using the microlocalization similar to that in a transcendental setting due to Kashiwara--Schapira works in the algebraic setting and prove partial positive results.

Keywords

characteristic cycles constructible sheaves microlocalization singular support positive characteristic

Cite

@article{arxiv.2607.17026,
  title  = {Characteristic cycles of constructible sheaves and microlocalization},
  author = {Takeshi Saito},
  journal= {arXiv preprint arXiv:2607.17026},
  year   = {2026}
}