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arXiv · 1910.03871

Minimal slope conjecture of $F$-isocrystals

Nobuo Tsuzuki
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Abstract

The minimal slope conjecture, which was proposed by K.Kedlaya, asserts that two irreducible overconvergent $F$-isocrystals on a smooth variety are isomorphic to each other if both minimal slope constitutions of slope filtrations are isomorphic to each other. We affirmatively solve the minimal slope conjecture for overconvergent $F$-isocrystals on curves and for overconvergent $\bar{\mathbb Q}_p$-$F$-isocrystals on smooth varieties over finite fields.

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Nobuo Tsuzuki. 2019-10-09. Minimal slope conjecture of $F$-isocrystals. https://arxiv.org/abs/1910.03871

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