A homotopy exact sequence for overconvergent isocrystals

Abstract

In this article we prove exactness of the homotopy sequence of overconvergent $p$-adic 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 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.

36 pages, final version

References in corpus (3)

• On Nori's Fundamental Group Scheme
• Relative Fundamental Groups and Rational Points
• The homotopy sequence of the algebraic fundamental group

Cited by in corpus (2)

• Crystalline Chebotarëv density theorems
• A crystalline incarnation of Berthelot's conjecture and Künneth formula for isocrystals