We prove constancy of Newton polygons of all convergent-isocrystals on Abelian varieties over finite fields. Applying the constancy, we prove the isotriviality of proper smooth families of curves over Abelian varieties. More generally, we prove the isotriviality over projective smooth varieties on which any convergent-isocrystal has constant Newton polygons.
|Number of pages||39|
|Journal||Journal of the Institute of Mathematics of Jussieu|
|Publication status||Published - 2021 Mar|