In this paper we present a classification of the possible upper ramification jumps for an elementary Abelian p-extension of ap-adic field. The fundamental step for the proof of the main result is the computation of the ramification filtration for the maximal elementary Abelian p-extension of the base field K. This result generalizes [3, Lemma 9, p. 2861, where the same result is proved under the assumption that K contains a primitive p-th root of unity. To deal with this general case we use class field theory and the explicit relations between the normic group of an extension and its ramification jumps, and we obtain necessary and sufficient conditions for the upper ramification jumps of an elementary Abelian p-extension of K.
A note on upper ramification jumps in Abelian extensions of exponent p / Capuano, L.; Del Corso, I.. - In: RIVISTA DI MATEMATICA DELLA UNIVERSITÀ DI PARMA (ONLINE). - ISSN 2284-2578. - 6:2(2015), pp. 317-329.
|Titolo:||A note on upper ramification jumps in Abelian extensions of exponent p|
|Data di pubblicazione:||2015|
|Appare nelle tipologie:||1.1 Articolo in rivista|