Foliations on Shimura varieties in positive characteristic

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Abstract
This paper is a continuation of a paper by de Shalit and Goren from 2018. We study foliations of two types on Shimura varieties S S in characteristic p p . The first, which we call tautological foliations , are defined on Hilbert modular varieties, and lift to characteristic 0 0 . The second, the V V -foliations , are defined on unitary Shimura varieties in characteristic p 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 p -closed, and the locus where they are smooth. Where not smooth, we construct a successive blowup 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 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 p , to S . S.
Funding Information
  • Natural Sciences and Engineering Research Council of Canada (RGPIN-2019-03909)
  • Natural Sciences and Engineering Research Council of Canada (276/17)
  • Israel Science Foundation (RGPIN-2019-03909)
  • Israel Science Foundation (276/17)

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