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Rank 2 $F$-isocrystals and abelian varieties Krishnamoorthy, Subrahmanya


We report on joint work-in-progress with Ambrus Pal on the following conjecture. Conjecture: Let $X$ be a smooth variety over a finite field $k$ and let $E$ be an overconvergent F-isocrystal on $X$ that has rank 2 and is absolutely irreducible. Suppose further that $E$ has "infinite monodromy at a divisor at infinity." Then $E$ comes from a family of abelian varieties.

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