A cut-by-curves criterion for overconvergent of F-isocrystals

2022/02/08 by Grubb, Thomas, Kedlaya, Kiran S., Upton, James
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2202.03604

Abstract

Let X be a smooth scheme over a finite field. It is conjectured that a convergent F-isocrystal on X is overconvergent if its restriction to every curve contained in X is overconvergent. Using the theory of étale and crystalline companions, we establish a weaker version of this criterion in which we also assume that the wild local monodromy of the restrictions to curves is trivialized by pullback along a single dominant morphism to X.

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