Reductions of non-lc ideals and non F-pure ideals assuming weak ordinarity

Abstract

Assume X is a variety over C, A ⊆ C is a finitely generated Zalgebra and X A a model of X (i.e. X A × A C ∼ = X). Assuming the weak ordinarity conjecture we show that there is a dense set S ⊆ Spec A such that for every closed point s of S the reduction of the maximal non-lc ideal filtration J (X, ∆, a λ ) coincides with the non-F -pure ideal filtration σ(Xs, ∆s, a λ s ) provided that (X, ∆) is klt or if (X, ∆) is log canonical, a is locally principal and the non-klt locus is contained in a.