Abstract

We give characterizations of test ideals and $F$-rational singularities via (regular) alterations. Formally, the descriptions are analogous to standard characterizations of multiplier ideals and rational singularities in characteristic zero via log resolutions. Lastly, we establish Nadel-type vanishing theorems (up to finite maps) for test ideals, and further demonstrate how these vanishing theorems may be used to extend sections.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 61-109
Launched on MUSE
2015-02-05
Open Access
No
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