A characteristic p analogue of plt singularities and adjoint ideals

2006/03/20 by Takagi, Shunsuke
#13A35 (Secondary) #14B05 (Primary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0603460

Abstract

We introduce a new variant of tight closure and give an interpretation of adjoint ideals via this tight closure. As a corollary, we prove that a log pair (X,Δ) is plt if and only if the modulo p reduction of (X,Δ) is divisorially F-regular for all large p ≫ 0. Here, divisorially F-regular pairs are a class of singularities in positive characteristic introduced by Hara and Watanabe in terms of Frobenius splitting.

Related

• Adjoint ideals and a correspondence between log canonicity and F-purity
• F-singularities in families
• Log canonical thresholds in positive characteristic
• Inversion of modulo p reduction and a partial descent from characteristic 0 to positive characteristic
• Singularities of pluri-theta divisors in Char p>0