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

2018/04/09 by Axel Stäbler, Stäbler, Axel
Mathematics · #Rings, Modules, and Algebras #Advanced Banach Space Theory #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1804.02922

Abstract

Assume X is a variety over \ℂ, A \⊆ \ℂ is a\nfinitely generated \ℤ-algebra and X_A a model of X (i.e. X_A\n\×_A \ℂ \≅ X). Assuming the weak ordinarity conjecture we show\nthat there is a dense set S \⊆ \Spec A such that for every\nclosed point s of S the reduction of the maximal non-lc ideal filtration\n\J'(X, \Δ, mathfraka^\λ) coincides with the non-F-pure\nideal filtration \σ(X_s, \Δ_s, mathfraka_s^\λ) provided that\n(X, \Δ) is klt or if (X, \Δ) is log canonical, mathfraka is\nprincipal and the non-klt locus is contained in mathfraka.\n

Related

• On a conjecture of Debs and Saint Raymond
• Good Reduction of Good Filtrations at Places
• Nonregular ideals
• The log canonical threshold and rational singularities
• Depth in a pathological case