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arXiv · 1611.03884

\'Etale fundamental groups of strongly $F$-regular schemes

Bhargav Bhatt·Javier Carvajal-Rojas·Patrick Graf·Karl Schwede·Kevin Tucker
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Abstract

We prove that a strongly $F$-regular scheme $X$ admits a finite, generically Galois, and \'etale-in-codimension-one cover $\widetilde X \to X$ such that the \'etale fundamental groups of $\widetilde X$ and $\widetilde X_{reg}$ agree. Equivalently, every finite \'etale cover of $\widetilde X_{reg}$ extends to a finite \'etale cover of $\widetilde X$. This is analogous to a result for complex klt varieties by Greb, Kebekus and Peternell.

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Bhargav Bhatt, Javier Carvajal-Rojas, Patrick Graf, Karl Schwede, Kevin Tucker. 2016-11-11. \'Etale fundamental groups of strongly $F$-regular schemes. https://doi.org/10.1093/imrn%2Frnx253

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