Vol. 7, No. 1, 2013

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editors' Interests Submission Guidelines Submission Form Editorial Login Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Galois module structure of local unit groups

Romyar Sharifi

Vol. 7 (2013), No. 1, 157–191
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 $Gal\left(K∕{ℚ}_{p}\right)$. 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
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