Polarizations and Grothendieck's standard conjectures

• 成果类型: Article
• 署名作者: Milne, JS
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062126
• 发表日期: 2002
• 页码: 599-610
• 关键词: varieties

摘要

We prove that Grothendieck's Hodge standard conjecture holds for abelian varieties in arbitrary characteristic if the Hodge conjecture holds for complex abelian varieties of CM-type. For abelian varieties with no exotic algebraic classes, we prove the Hodge standard conjecture unconditionally.