Galois module structure of local unit groups

Sharifi, Romyar

doi:10.2140/ant.2013.7.157

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Galois module structure of local unit groups

Romyar Sharifi

Vol. 7 (2013), No. 1, 157–191

DOI: 10.2140/ant.2013.7.157

Abstract

We study the groups $U_{i}$ in the unit filtration of a finite abelian extension $K$ of $ℚ_{p}$ for an odd prime $p$ . We determine explicit generators of the $U_{i}$ as modules over the $ℤ_{p}$ -group ring of $Gal (K ∕ ℚ_{p})$ . We work in eigenspaces for powers of the Teichmüller character, first at the level of the field of norms for the extension of $K$ by $p$ -power roots of unity and then at the level of $K$ .

Keywords

Galois module structure, unit filtration, local field

Mathematical Subject Classification 2010

Primary: 11SXX

Milestones

Received: 20 August 2011

Revised: 29 November 2011

Accepted: 20 February 2012

Published: 28 March 2013

Authors

Romyar Sharifi
Department of Mathematics University of Arizona 617 N. Santa Rita Ave PO Box 210089 Tucson AZ 85721-0089 United States
http://math.arizona.edu/~sharifi

Vol. 7, No. 1, 2013