Introduction ; Crys-stable bundles ; Torally Crys-stable bundles in positive characteristic ; VF-patterns ; Construction of examples ; Combinatorialization at infinity of the stack of nilcurves ; The stack of quasi-analytic self-isogenies ; The generalized ordinary theory ; The geometrization of binary-ordinary Frobenius liftings ; The geometrization of spiked Frobenius liftings ; Representations of the fundamental group of the curve ; Ordinary stable bundles on a curve