Geodesic
Slopes of $F$-isocrystals over abelian varieties
Documenta mathematica, Tome 28 (2023) no. 1, pp. 1-9 Cet article a éte moissonné depuis la source EMS Press

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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 
@article{10_4171_dm_910,
     author = {Marco D{\textquoteright}Addezio},
     title = {Slopes of $F$-isocrystals over abelian varieties},
     journal = {Documenta mathematica},
     pages = {1--9},
     year = {2023},
     volume = {28},
     number = {1},
     doi = {10.4171/dm/910},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/910/}
}
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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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