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.
Capuano, L., Del Corso, I. (2015). A note on upper ramification jumps in Abelian extensions of exponent p. RIVISTA DI MATEMATICA DELLA UNIVERSITÀ DI PARMA, 6(2), 317-329.
A note on upper ramification jumps in Abelian extensions of exponent p
Capuano L.;
2015-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
