Fundamental groups of $F$-regular singularities via $F$-signature
| Autor: | Carvajal-Rojas, Javier, Schwede, Karl, Tucker, Kevin |
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| Rok vydání: | 2016 |
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| Zdroj: | Ann. Sci. \'Ec. Norm. Sup\'er. (4) 51 (2018), no. 4, 993-1016 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.24033/asens.2370 |
| Popis: | 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. Comment: 22 pages, comments welcome |
| Databáze: | arXiv |
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