The delta isocrystal of Borger-Saha is isomorphic to the smallest filtered sub-isocrystal of crystalline cohomology for abelian schemes over p-adic rings, governed by order-1 delta characters.
Buium Differential modular forms attached to newforms modpJournal Number Theory 155 (2015), 111-128
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Delta characters and crystalline cohomology of abelian schemes
The delta isocrystal of Borger-Saha is isomorphic to the smallest filtered sub-isocrystal of crystalline cohomology for abelian schemes over p-adic rings, governed by order-1 delta characters.