Étale Fundamental Groups of Strongly $\boldsymbol{F}$-Regular Schemes. (30th October 2017)

• Record Type: Journal Article
• Authors: Bhatt, Bhargav; Carvajal-Rojas, Javier; Graf, Patrick; Schwede, Karl; Tucker, Kevin
• Is Part Of: International mathematics research notices. Volume 2019:Number 14(2019)
• Page Start: 4325
• Page End: 4339
• Publication Date: 2017-10-30
• Subjects: 14F35 -- 14F20 -- 14E20 -- 14F18 -- 14B05 -- 13A35 -- 13B40; Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx253
• Languages: English
• ISSNs: 1073-7928

Abstract

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 $\tilde X_{{\mathrm{reg}}}$ agree. Equivalently, every finite étale cover of $\tilde X_{{\mathrm{reg}}}$ extends to a finite étale cover of $\tilde X$ . This is analogous to a result for complex klt varieties by Greb, Kebekus, and Peternell.