Cohomological Milnor formula and Saito's conjecture on characteristic classes

• 成果类型: Article
• 署名作者: Yang, Enlin; Zhao, Yigeng
• 署名单位: Peking University; Westlake University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01319-y
• 发表日期: 2025
• 页码: 123-191
• 关键词: characteristic cycle; THEOREM

摘要

We confirm the quasi-projective case of Saito's conjecture (Invent. Math. 207:597-695, 2017), 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.