#### 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
##### 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