Cohomological Milnor formula and Saito's conjecture on characteristic classes
Algebraic Geometry
2025-02-18 v4 Number Theory
Abstract
We confirm the quasi-projective case of Saito's conjecture, namely that the cohomological characteristic classes defined by Abbes and Saito can be computed in terms of the characteristic cycles. We construct a cohomological characteristic class supported on the non-acyclicity locus of a separated morphism relatively to a constructible sheaf. As applications of the functorial properties of this class, we prove cohomological analogs of the Milnor formula and the conductor formula for constructible sheaves on (not necessarily smooth) varieties.
Keywords
Cite
@article{arxiv.2209.11086,
title = {Cohomological Milnor formula and Saito's conjecture on characteristic classes},
author = {Enlin Yang and Yigeng Zhao},
journal= {arXiv preprint arXiv:2209.11086},
year = {2025}
}
Comments
Final version. Note that the numbering of sections, propositions, and formulas in the arXiv version is different from that in the journal version