A homotopy exact sequence for overconvergent isocrystals. (25th October 2021)

• Record Type: Journal Article
• Authors: Lazda, Christopher; Pál, Ambrus
• Is Part Of: Forum of mathematics. Volume 9(2021)
• Publication Date: 2021-10-25
• Subjects: 14F35 -- 14F30; rigid cohomology -- homotopy exact sequence -- overconvergent isocrystals; Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2021.63
• Languages: English
• ISSNs: 2050-5094

Abstract

Abstract: In this article we prove exactness of the homotopy sequence of overconvergent fundamental groups for a smooth and projective morphism in characteristic p . We do so by first proving a corresponding result for rigid analytic varieties in characteristic $0$, following dos Santos [dS15] in the algebraic case. In characteristic p, we then proceed by a series of reductions to the case of a liftable family of curves, where we can apply the rigid analytic result. We then use this to deduce a Lefschetz hyperplane theorem for convergent fundamental groups, as well as a comparison theorem with the étale fundamental group.