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- W2913354315 abstract "Let $X_0$ be a smooth geometrically connected variety defined over a finite field $mathbb F_q$ and let $mathcal E_0^{dagger}$ be an irreducible overconvergent $F$-isocrystal on $X_0$. We show that if a subobject of minimal slope of the underlying convergent F-isocrystal $mathcal E_0$ admits a non-zero morphism to $mathcal O_{X_0}$ as convergent isocrystal, then $mathcal E_0^{dagger}$ is isomorphic to $mathcal O^{dagger}_{X_0}$ as 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 $mathcal E_0^{dagger}$ and the subgroup defined by $mathcal E_0$. 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-N'eron and answers positively a question of Esnault." @default.
- W2913354315 created "2019-02-21" @default.
- W2913354315 creator A5000120249 @default.
- W2913354315 creator A5004055703 @default.
- W2913354315 date "2022-01-06" @default.
- W2913354315 modified "2023-09-30" @default.
- W2913354315 title "Maximal tori of monodromy groups of $F$-isocrystals and an application to abelian varieties" @default.
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