Parabolicity conjecture of $F$-isocrystals

Abstract

In this article we prove Crew's parabolicity conjecture of $F$-isocrystals. For this purpose, we introduce and study the notion of $†$-hull of a sub-$F$-isocrystal. On the way, we prove a new Lefschetz theorem for overconvergent $F$-isocrystals.

30 pages; final version, to appear in Annals of Mathematics

References in corpus (1)

• Scalar Extension of Abelian and Tannakian Categories

Cited by in corpus (4)

• Boundedness of the $p$-primary torsion of the Brauer group of an abelian variety
• On the ordinary Hecke orbit conjecture
• Perfect points of abelian varieties
• Finiteness and cofiniteness of fine Selmer groups over function fields