The existence of an abelian variety over (Q)over-bar isogenous to no Jacobian

• 成果类型: Article
• 署名作者: Tsimerman, Jacob
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.176.1.12
• 发表日期: 2012
• 页码: 637-650
• 关键词: equidistribution; monodromy

摘要

We prove the existence of an abelian variety A of dimension g over (Q) over bar that is not isogenous to any Jacobian, subject to the necessary condition g > 3. Recently, C. Chai and F. Oort gave such a proof assuming the Andre-Oort conjecture. We modify their proof by constructing a special sequence of CM points for which we can avoid any unproven hypotheses. We make use of various techniques from the recent work of Klingler-Yafaev et al.