We prove a characteristic p analogue 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 characteristic p by 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.

中文翻译：

---

特征 p 中反常滑轮的茎的边界和 Shende 和 Tsimerman 的猜想

我们证明了梅西 (Massey) 的结果的特征 p 类似物，它根据该捆的特征循环的某些交集多重性来限制反常捆的茎的维度。这使用了 Saito 在特征 p 中构造反常层的特征循环。我们应用这个来证明 Shende 和 Tsimerman 对超椭圆雅可比中 theta 轨迹的两个平移的交集的 Betti 数的猜想。这意味着 Michel-Venkatesh 混合猜想的函数场模拟，关于 CM 点在两条模曲线的乘积上的等分布。