Étale fundamental groups of strongly $F$-regular schemes

Abstract

We prove that a strongly $F$-regular scheme $X$ admits a finite, generically Galois, and étale-in-codimension-one cover $\tilde{X}\to X$ 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.

10 pages, comments welcome

References in corpus (2)

• F-signature and Hilbert-Kunz Multipicity: a combined approach and comparison
• Upper semi-continuity of the Hilbert-Kunz multiplicity

Cited by in corpus (5)

• Polarized endomorphisms of normal projective threefolds in arbitrary characteristic
• The local fundamental group of a Kawamata log terminal singularity is finite
• On tame ramification and centers of $F$-purity
• On the local étale fundamental group of KLT threefold singularities
• Étale coverings in codimension 1 with applications to Mori Dream Spaces