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

Thomas Grubb, Kiran S. Kedlaya, James Upton

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 ov…