Year: 2011
Type: preprint
Abstract: 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 $π_* ω_Y \to ω_X$ for every such alteration $π\: Y \to X$. 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.
Source: arXiv (Cornell University)
Authors: Blickle, Manuel, Schwede, Karl, Tucker, Kevin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Singularities in Characteristic Zero and Singularities in Positive Characteristic, Frobenius singularities and related invariants, PostDoctoral Research Fellowship, PostDoctoral Research Fellowship, FRG: Collaborative Research: Birational Geometry and Singularities in Zero and Positive Characteristic, G6671297155, G8377667862, CAREER: Test Ideals and the Geometry of Projective Varieties in Positive Characteristic
OpenAlex ID: W2951613664