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• W2432420006 abstract "We prove that the local etale fundamental group of a strongly $F$-regular singularity is finite (and likewise for the 'etale fundamental group of the complement of a codimension $geq 2$ set), analogous to results of Xu and Greb-Kebekus-Peternell for KLT singularities in characteristic zero. In fact our result is effective, we show that the reciprocal of the $F$-signature of the singularity gives a bound on the size of this fundamental group. To prove these results and their corollaries, we develop new transformation rules for the $F$-signature under finite etale-in-codimension-one extensions. As another consequence of these transformation rules, we also obtain purity of the branch locus over rings with mild singularities (particularly if the $F$-signature is $> 1/2$). Finally, we generalize our $F$-signature transformation rules to the context of pairs and not-necessarily etale-in-codimension-one extensions, obtaining an analog of another result of Xu." @default.
• W2432420006 created "2016-06-24" @default.
• W2432420006 creator A5034640542 @default.
• W2432420006 creator A5036493678 @default.
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• W2432420006 date "2018-01-01" @default.
• W2432420006 modified "2023-09-30" @default.
• W2432420006 title "Fundamental groups of F-regular singularities via F-signature" @default.
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• W2432420006 doi "https://doi.org/10.24033/asens.2370" @default.
• W2432420006 hasPublicationYear "2018" @default.
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