2022/05/02 by Goren, Eyal Z., de Shalit, Ehud
#11G18 #14G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2205.00702
This paper is a continuation of [G-dS1]. We study foliations of two types on Shimura varieties S in characteristic p. The first, which we call "tautological foliations", are defined on Hilbert modular varieties, and lift to characteristic 0. The second, the "V-foliations", are defined on unitary Shimura varieties in characteristic p only, and generalize the foliations studied by us before, when the CM field in question was quadratic imaginary. We determine when these foliations are p-closed, and the locus where they are smooth. Where not smooth, we construct a "successive blow up" of our Shimura variety to which they extend as smooth foliations. We discuss some integral varieties of the foliations. We relate the quotient of S by the foliation to a purely inseparable map from a certain component of another Shimura variety of the same type, with parahoric level structure at p, to S.