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Let $k$ be a complete discretely valued field of equal characteristic $p > 0$with possibly imperfect residue field and let $G_k$ be its Galois group. Weprove that the conductors computed by the arithmetic ramification filtrationson $G_k$ coincide with the differential Artin conductors and Swan conductors ofGalois representations of $G_k$. As a consequence, we give a Hasse-Arf theoremfor arithmetic ramification filtrations in this case. As applications, weobtain a Hasse-Arf theorem for finite flat group schemes; we also give acomparison theorem between the differential Artin conductors and Borger'sconductors.

On ramification filtrations andp-adic differential modules, I: the equal characteristic case