Upper ramification jumps in abelian extensions of exponent p
Abstract
In this paper we present a classification of the possible upper ramification jumps for an elementary abelian pextension of a padic field. The fundamental step for the proof of the main result is the computation of the ramification filtration for the maximal elementary abelian pextension of the base field K. This is a generalization of a previous work of the second author and Dvornicich where the same result is proved under the assumption that K contains a primitive pth root of unity. Using the class field theory and the explicit relations between the normic group of an extension and its ramification jumps, it is fairly simple to recover necessary and sufficient conditions for the upper ramification jumps of an elementary abelian pextension of K.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 DOI:
 10.48550/arXiv.1407.2496
 arXiv:
 arXiv:1407.2496
 Bibcode:
 2014arXiv1407.2496C
 Keywords:

 Mathematics  Number Theory;
 11S15
 EPrint:
 9 pages