The characteristic cycle and the singular support of a constructible sheaf

• 成果类型: Article
• 署名作者: Saito, Takeshi
• 署名单位: University of Tokyo
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0675-3
• 发表日期: 2017
• 页码: 597-695
• 关键词: ramification; VARIETIES

摘要

We define the characteristic cycle of an ,tale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by Beilinson. We prove a formula A la Milnor for the total dimension of the space of vanishing cycles and an index formula computing the Euler-Poincar, characteristic, generalizing the Grothendieck-Ogg-Shafarevich formula to higher dimension. An essential ingredient of the construction and the proof is a partial generalization to higher dimension of the semi-continuity of the Swan conductor due to Deligne-Laumon. We prove the index formula by establishing certain functorial properties of characteristic cycles.