Vol. 7, No. 1, 2013

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Galois module structure of local unit groups

Romyar Sharifi

Vol. 7 (2013), No. 1, 157–191

We study the groups Ui in the unit filtration of a finite abelian extension K of p for an odd prime p. We determine explicit generators of the Ui as modules over the p-group ring of Gal(Kp). 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.

Galois module structure, unit filtration, local field
Mathematical Subject Classification 2010
Primary: 11SXX
Received: 20 August 2011
Revised: 29 November 2011
Accepted: 20 February 2012
Published: 28 March 2013
Romyar Sharifi
Department of Mathematics
University of Arizona
617 N. Santa Rita Ave
PO Box 210089
Tucson AZ 85721-0089
United States