2011/07/19 by Manuel Blickle, Blickle, Manuel, Karl Schwede +3 · 2 citations
Computer Science · Mathematics · #13A35 #14B05 #14E15 #14F17 #14F18 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Boundary (topology) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Discrete mathematics #Divisor (algebraic geometry) #FOS: Mathematics #Gravitational singularity #Ideal (ethics) #Mathematical analysis #Mathematics #Multiplier (economics) #Omega #Physics #Polynomial and algebraic computation #Pure mathematics #TRACE (psycholinguistics) #Variety (cybernetics) #Zero (linguistics) #math.AC #math.AG #msc:13A35 #msc:14B05 #msc:14E15 #msc:14F17 #msc:14F18
paper · pdf · doi:10.48550/arxiv.1107.3807
38 pages, typos corrected, references updated and improved exposition. To appear in the American Journal of Mathematics
openalex publication_date 2011/07/19 · arxiv created 2014/05/05 · arxiv updated 2014/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For a normal F-finite variety X and a boundary divisor Δ we give a uniform description of an ideal which in characteristic zero yields the multiplier ideal, and in positive characteristic the test ideal of the pair (X,Δ). Our description is in terms of regular alterations over X, and one consequence of it is a common characterization of rational singularities (in characteristic zero) and F-rational singularities (in characteristic p) by the surjectivity of the trace map π_* ωY → ωX for every such alteration π Y → X. Furthermore, building on work of B. Bhatt, we establish up-to-finite-map versions of Grauert-Riemenscheneider and Nadel/Kawamata-Viehweg vanishing theorems in the characteristic p setting without assuming W2 lifting, and show that these are strong enough in some applications to extend sections.