Ramification of Some Automorphisms of Local Fields Original Research Article

Letkbe a perfect field of characteristicpand letγset membership, variantAut(k((t))). Define the ramification numbers ofγbyim=vt(γpm(t)−t)−1. We give a characterization of the sequences (im) which are the sequences of ramification numbers of infinite order automorphisms of formal power series fields over finite fields. Then, given a perfect field k, we give sufficient conditions on (im) to be the sequence of ramification numbers of an autormorphismγset membership, variantAutk(k((t))) and we investigate these sequences (im) in the case where there existsσset membership, variantAutk(k((t))) such thatσγ=γσwithσ≠γνfor allνset membership, variantimagep.