Étale Fundamental Groups of Strongly $\boldsymbol{F}$-Regular Schemes. (30th October 2017) - Bhatt, Bhargav; Carvajal-Rojas, Javier; Graf, Patrick; Schwede, Karl; Tucker, Kevin
Abstract: We prove that a strongly $F$ -regular scheme $X$ admits a finite, generically Galois, and étale-in-codimension-one cover $\tilde X → X$ such that the étale fundamental groups of $\tilde X$ and $\tilde X_{{reg}}$ agree. Equivalently, every finite étale cover of $\tilde X_{{reg}}$ extends to a finite étale cover of $\tilde X$ . This is analogous to a result for complex klt varieties by Greb, Kebekus, and Peternell.