Bogomolov's inequality for Higgs sheaves in positive characteristic

• 成果类型: Article
• 署名作者: Langer, Adrian
• 署名单位: University of Warsaw
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0534-z
• 发表日期: 2015
• 页码: 889-920
• 关键词: characteristic-p; vector-bundles; SURFACES; semistability; conjecture; MODULES

摘要

We prove Bogomolov's inequality for Higgs sheaves on varieties in positive characteristic p that can be lifted modulo p(2). This implies the Miyaoka-Yau inequality on surfaces of non-negative Kodaira dimension liftable modulo p(2). This result is a strong version of Shepherd-Barron's conjecture. Our inequality also gives the first algebraic proof of Bogomolov's inequality for Higgs sheaves in characteristic zero, solving the problem posed by Narasimhan.