Supersingular K3 surfaces are unirational

• 成果类型: Article
• 署名作者: Liedtke, Christian
• 署名单位: Technical University of Munich
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0547-7
• 发表日期: 2015
• 页码: 979-1014
• 关键词: tate-conjecture

摘要

We show that supersingular K3 surfaces in characteristic are related by purely inseparable isogenies. This implies that they are unirational, which proves conjectures of Artin, Rudakov, Shafarevich, and Shioda. As a byproduct, we exhibit the moduli space of rigidified K3 crystals as an iterated -bundle over . To complete the picture, we also establish Shioda-Inose type isogeny theorems for K3 surfaces with Picard rank in positive characteristic.