What is "isocrystal"

In algebraic geometry, isocrystals are p-adic analogues of Q-adic étale sheaves, introduced by (though the definition of isocrystal only appears in part II of this paper by ). The term isocrystal stands for roughly " crystal up to isogeny". Convergent isocrystals are a variation of isocrystals that work better over non-perfect fields, and overconvergent isocrystals are another variation related to overconvergent cohomology theories.