Geodesic
The $p$-adic monodromy group of abelian varieties over global function fields of characteristic $p$
Documenta mathematica, Tome 27 (2022), pp. 1509-1579 Cet article a éte moissonné depuis la source EMS Press

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We prove an analogue of the Tate isogeny conjecture and the semi-simplicity conjecture for overconvergent crystalline Dieudonné modules of abelian varieties defined over global function fields of characteristic p. As a corollary we deduce that monodromy groups of such overconvergent crystalline Dieudonné modules are reductive, and after a finite base change of coefficients their connected components are the same as the connected components of monodromy groups of Galois representations on the corresponding l-adic Tate modules, for l different from p. We also show such a result for general compatible systems incorporating overconvergent F-isocrystals, conditional on a result of Abe.
DOI : 10.4171/dm/903
Classification : 14F30, 14F35, 14K15
Mots-clés : monodromy, F-isocrystals, overconvergent crystalline Dieudonné modules 
@article{10_4171_dm_903,
     author = {Ambrus P\'al},
     title = {The $p$-adic monodromy group of abelian varieties over global function fields of characteristic $p$},
     journal = {Documenta mathematica},
     pages = {1509--1579},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/903},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/903/}
}
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Ambrus Pál. The $p$-adic monodromy group of abelian varieties over global function fields of characteristic $p$. Documenta mathematica, Tome 27 (2022), pp. 1509-1579. doi: 10.4171/dm/903

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