In this paper we present a classification of the possible upper ramification jumps for an elementary abelian $p$-extension of a $p$-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 \cite[Lemma 9, p. 286]{Del_Corso_Dvornicich_2007}, 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 $K$.

Upper ramification jumps in abelian extensions of exponent p / CAPUANO L.; DEL CORSO I.. - In: RIVISTA DI MATEMATICA DELLA UNIVERSITÀ DI PARMA. - ISSN 0035-6298. - STAMPA. - 6:2(2015), pp. 317-329.

Upper ramification jumps in abelian extensions of exponent p

DEL CORSO, ILARIA
2015

Abstract

In this paper we present a classification of the possible upper ramification jumps for an elementary abelian $p$-extension of a $p$-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 \cite[Lemma 9, p. 286]{Del_Corso_Dvornicich_2007}, 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, Ilaria
File in questo prodotto:
File Dimensione Formato  
Parma2015.pdf

solo utenti autorizzati

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 405.34 kB
Formato Adobe PDF
405.34 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/426867
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? ND
social impact