Bounds for the stalks of perverse sheaves in characteristic p and a conjecture of Shende and Tsimerman

Autor:	Sawin, Will, Tsimerman, Jacob
Rok vydání:	2019
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1907.04850 Zobrazit plný text záznamu View this record from Arxiv