Characteristic cycles and non-acyclicity classes for constructible étale sheaves

@misc{bao2026characteristic,
  title = {{Characteristic cycles and non-acyclicity classes for constructible étale sheaves}},
  author = {Kaicheng Bao and Jiangnan Xiong and Enlin Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25732},
  eprint = {2610.25732},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25732},
  note = {CC0},
}

TY  - UNPB
TI  - Characteristic cycles and non-acyclicity classes for constructible étale sheaves
AU  - Kaicheng Bao
AU  - Jiangnan Xiong
AU  - Enlin Yang
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25732
UR  - https://arxiv.org/abs/2610.25732
AB  - Let f:X→ Y be a morphism between smooth schemes over a perfect field k. Let ℱ be a constructible sheaf on X and Z a closed subscheme of X such that f is SS(ℱ)-transversal outside Z. We construct a class supported on the non-transversal locus Z by using the characteristic cycle CC(ℱ) defined by T. Saito. This class is a geometric counterpart of the non-acyclicity class introduced by the third author and Zhao in [Invent. Math. 240 (2025), 123-191]. Under certain conditions, the formation of this class is compatible with base change and proper pushforward. It also satisfies the Milnor formula and a conductor formula. We conjecture that the image of this geometric class under the cycle class map is the non-acyclicity class. This conjecture can be viewed as a (relative version of) Milnor-type formula for non-isolated singularities. We prove this conjecture when k is algebraically closed, X is quasi-affine and Y=𝔸^1_k.
ER  -