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.

arXiv comment30 pages; final version, to appear in Annals of Mathematics

References in corpus (7)

• Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations
• The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields
• Full faithfulness for overconvergent F-isocrystals
• The monodromy groups of lisse sheaves and overconvergent $F$-isocrystals
• On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic II
• Scalar Extension of Abelian and Tannakian Categories
• Maximal tori of monodromy groups of $F$-isocrystals and an application to abelian varieties

Cited by in corpus (5)

• Maximal tori of monodromy groups of $F$-isocrystals and an application to abelian varieties
• 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