On ramification filtrations and p-adic differential modules, I: equal characteristic case
نویسنده
چکیده
Let k be a complete discretely valued field of equal characteristic p > 0 with possibly imperfect residue field and let Gk be its Galois group. We prove that the conductors computed by the arithmetic ramification filtrations on Gk defined in [3] coincide with the differential Artin conductors and Swan conductors of Galois representations of Gk defined in [17]. As a consequence, we give a Hasse-Arf theorem for arithmetic ramification filtrations in this case. As applications, we obtain a Hasse-Arf theorem for finite flat group schemes; we also give a comparison theorem between the differential Artin conductors and Borger’s conductors [8].
منابع مشابه
On Ramification Filtrations and p-adic Differential Equations, I
Let k be a complete discrete valuation field of equal characteristic p > 0 with possibly imperfect residue field. Let Gk be its Galois group. We will prove that the conductors computed by the arithmetic ramification filtrations on Gk defined in [2] coincide with the differential Artin conductors and Swan conductors of Galois representations of Gk defined in [15]. As a consequence, we give a Has...
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