On ramification filtrations and $p$adic differential modules, I: equal characteristic case
Abstract
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. We prove that the conductors computed by the arithmetic ramification filtrations on $G_k$ coincide with the differential Artin conductors and Swan conductors of Galois representations of $G_k$. As a consequence, we give a HasseArf theorem for arithmetic ramification filtrations in this case. As applications, we obtain a HasseArf theorem for finite flat group schemes; we also give a comparison theorem between the differential Artin conductors and Borger's conductors.
 Publication:

arXiv eprints
 Pub Date:
 January 2008
 DOI:
 10.48550/arXiv.0801.4962
 arXiv:
 arXiv:0801.4962
 Bibcode:
 2008arXiv0801.4962X
 Keywords:

 Mathematics  Number Theory
 EPrint:
 Improvement on some of the proofs following the suggestion of the referee