Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields

• 成果类型: Article
• 署名作者: Ellenberg, Jordan S.; Venkatesh, Akshay; Westerland, Craig
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.183.3.1
• 发表日期: 2016
• 页码: 729-786
• 关键词: quadratic function-fields; mapping class-groups; number-fields; heuristics; CURVES; EXTENSIONS; monodromy; TOPOLOGY; roots; unity

摘要

We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let l > 2 be prime and A a finite abelian l-group. Then there exists Q = Q(A) such that, for q greater than Q, a positive fraction of quadratic extensions of F-q(t) have the l-part of their class group isomorphic to A.