Algebra & Number Theory

Galois module structure of local unit groups

Romyar Sharifi

Abstract

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

Article information

Source
Algebra Number Theory, Volume 7, Number 1 (2013), 157-191.

Dates
Revised: 29 November 2011
Accepted: 20 February 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513729932

Digital Object Identifier
doi:10.2140/ant.2013.7.157

Mathematical Reviews number (MathSciNet)
MR3037893

Zentralblatt MATH identifier
1319.11087

Subjects
Primary: 11SXX

Citation

Sharifi, Romyar. Galois module structure of local unit groups. Algebra Number Theory 7 (2013), no. 1, 157--191. doi:10.2140/ant.2013.7.157. https://projecteuclid.org/euclid.ant/1513729932

References

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