• Corpus ID: 231627731

Slopes of $F$-isocrystals over abelian varieties

@inproceedings{dAddezio2021SlopesO,
  title={Slopes of \$F\$-isocrystals over abelian varieties},
  author={Marco d’Addezio},
  year={2021}
}
We prove that an F -isocrystal over an abelian variety defined over a perfect field of positive characteristic has constant slopes. This recovers and extends a theorem of Tsuzuki for abelian varieties over finite fields. Our proof exploits the theory of monodromy groups of convergent isocrystals. 
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A crystalline incarnation of Berthelot’s conjecture and Künneth formula for isocrystals
Berthelot’s conjecture predicts that under a proper and smooth morphism of schemes in characteristic p p , the higher direct images of an overconvergent F F -isocrystal are…

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