Geodesic
Slopes of $F$-isocrystals over abelian varieties
Documenta mathematica, Tome 28 (2023) no. 1, pp. 1-9

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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.
DOI : 10.4171/dm/910
Classification : 14F30, 11G10, 14K05
Mots-clés : F-isocrystal, slope filtration, abelian variety 
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     author = {Marco D{\textquoteright}Addezio},
     title = {Slopes of $F$-isocrystals over abelian varieties},
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Marco D’Addezio. Slopes of $F$-isocrystals over abelian varieties. Documenta mathematica, Tome 28 (2023) no. 1, pp. 1-9. doi: 10.4171/dm/910

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