F-singularities via alterations

By Manuel Blickle, Karl Schwede, Kevin Tucker. 2011

56 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/25569dadabef1e08a7739099633cd5a861602550

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

A canonical linear system associated to adjoint divisors in characteristic $p > 0$ (2011, methodology): “L) where the ﬁrst intersection runs over all ﬁnite maps f: Y −→ Xof irreducible varieties (note it is harmless to only consider reduced or even normal Y). This ﬁrst linear system T0 was explored in [BST11] where it was used to construct transformation rules for test ideals under birational maps. No”
ON THE BEHAVIOR OF TEST IDEALS UNDER FINITE MORPHISMS (2010, unknown): “endices that appeared in previous versions. It removes an appendix dealing with the behavior of multiplier ideals in positive characteristic. This material has been incorporated into a separate paper [BST11], joint with Manuel Blickle. The other appendix, on explicitly lifting ﬁnite maps under tame ”