The main aim of this article is to construct a canonical $F$-isocrystal ${fH}(A)_K$ for an abelian scheme $A$ over a $p$-adic complete discrete valuationring of perfect residue field. This $F$-isocrystal ${f H}(A)_K$ comes with afiltration and admits a natural map to the usual Hodge sequence of $A$. Eventhough ${f H}(A)_K$ admits a map to the crystalline cohomology of $A$, the$F$-structure on ${f H}(A)_K$ is fundamentally distinct from the one on thecrystalline cohomology. When $A$ is an elliptic curve, we further show that${f H}(A)$ itself is an $F$-crystal and that implies a strengthened versionof Buium's result on differential characters.
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机译：本文的主要目标是构建一个规范$ f $ -isocrystal $ { bfh}（a）_k $ for a abelian计划$ a $ a $ a超过完美的残留场的每次$ p $ theat全离散的律值。此$ f $ -isocrystal $ { bf h}（a）_k $附带在上方并承认自然地图到$ a $的常规霍奇序列。 Femenhough $ { bf h}（a）_k $概述了$ a $的晶体正交学的地图，$ f $ -structure on $ { bf h}（a）_k $基本上不同于thecrystalline同步学。当$ a $是一个椭圆曲线时，我们进一步显示$ { bf h}（a）$本身是$ f $ -crystal，这意味着Buium在差分字符上得到了增强的versionof。
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