Bounds for the stalks of perverse sheaves in characteristicpand a conjecture of Shende and Tsimerman
成果类型：
Article
署名作者：
Sawin, Will
署名单位：
Columbia University
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-020-01006-0
发表日期：
2021
页码：
1-32
关键词：
摘要：
We prove a characteristicpanalogue of a result of Massey which bounds the dimensions of the stalks of a perverse sheaf in terms of certain intersection multiplicities of the characteristic cycle of that sheaf. This uses the construction of the characteristic cycle of a perverse sheaf in characteristicpby Saito. We apply this to prove a conjecture of Shende and Tsimerman on the Betti numbers of the intersections of two translates of theta loci in a hyperelliptic Jacobian. This implies a function field analogue of the Michel-Venkatesh mixing conjecture about the equidistribution of CM points on a product of two modular curves.
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