Semistable sheaves in positive characteristic

• 成果类型: Article
• 署名作者: Langer, A
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.159.251
• 发表日期: 2004
• 页码: 251-276
• 关键词: vector-bundles; characteristic-p; SURFACES; families

摘要

We prove Maruyama's conjecture on the boundedness of slope semistable sheaves on a projective variety defined over a noetherian ring. Our approach also gives a new proof of the boundedness for varieties defined over a characteristic zero field. This result implies that in mixed characteristic the moduli spaces of Gieseker semistable sheaves are projective schemes of finite type. The proof uses a new inequality bounding slopes of the restriction of a sheaf to a hypersurface in terms of its slope and the discriminant. This inequality also leads to effective restriction theorems in all characteristics, improving earlier results in characteristic zero.