Abstract
Let be a complete discretely valued field of equal characteristic with possibly imperfect residue field, and let be its Galois group. We prove that the conductors computed by the arithmetic ramification filtrations on defined by Abbes and Saito (Amer. J. Math 124:5, 879–920) coincide with the differential Artin conductors and Swan conductors of Galois representations of defined by Kedlaya (Algebra Number Theory 1:3, 269–300). As a consequence, we obtain 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 (Math. Ann. 329:1, 1–30).
Citation
Liang Xiao. "On ramification filtrations and $p$-adic differential modules, I: the equal characteristic case." Algebra Number Theory 4 (8) 969 - 1027, 2010. https://doi.org/10.2140/ant.2010.4.969
Information