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- Title
Maximal tori of monodromy groups of F-isocrystals and an application to abelian varieties.
- Authors
Ambrosi, Emiliano; D'Addezio, Marco
- Abstract
Let X0 be a smooth geometrically connected variety defined over a finite field Fq, and let Ey0 be an irreducible overconvergent F-isocrystal on X0. We show that if a subobject of minimal slope of the associated convergent F-isocrystal E0 admits a nonzero morphism to OX0 as a convergent isocrystal, then Ey 0 is isomorphic to Oy X0 as an overconvergent isocrystal. This proves a special case of a conjecture of Kedlaya. The key ingredient in the proof is the study of the monodromy group of Ey 0 and of the subgroup dned by E0. The new input in this setting is that the subgroup contains a maximal torus of the entire monodromy group. This is a consequence of the existence of a Frobenius torus of maximal dimension. As an application, we prove a finiteness result for the torsion points of abelian varieties, which extends the previous theorem of Lang-Neron and answers positively a question of Esnault.
- Subjects
MONODROMY groups; GEOMETRY; MATHEMATICAL models; MORPHISMS (Mathematics); ABELIAN functions
- Publication
Algebraic Geometry, 2022, Vol 9, Issue 5, p633
- ISSN
2313-1691
- Publication type
Article
- DOI
10.14231/AG-2022-019