Computing the torsion of the $p$-ramified module of a number field
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- by Frédéric Pitoun and Firmin Varescon PDF
- Math. Comp. 84 (2015), 371-383 Request permission
Abstract:
We fix a prime number $p$ and a number field $K$, and denote by $M$ the maximal abelian $p$-extension of $K$ unramified outside $p$. Our aim is to study the $\mathbb {Z}_p$-module $\mathfrak {X}=\mathrm {Gal}(M/K)$ and to give a method to effectively compute its structure as a $\mathbb {Z}_p$-module. We also give numerical results, for real quadratic fields, cubic fields and quintic fields, together with their interpretations via Cohen-Lenstra heuristics.References
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Additional Information
- Frédéric Pitoun
- Affiliation: 27 Avenue du 8 mai 1945, 11400 Castelnaudary, France
- Email: frederic.pitoun@free.fr
- Firmin Varescon
- Affiliation: Laboratoire de mathématiques de Besançon, CNRS UMR 6623, Université de Franche Comté, 16 Route de Gray, 25020 Besançon Cédex, France
- Email: firmin.varescon@univ-fcomte.fr
- Received by editor(s): April 10, 2012
- Received by editor(s) in revised form: February 13, 2013, April 4, 2013, and May 3, 2013
- Published electronically: June 24, 2014
- © Copyright 2014 American Mathematical Society
- Journal: Math. Comp. 84 (2015), 371-383
- MSC (2010): Primary 11R23, 11R37, 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-2014-02838-X
- MathSciNet review: 3266966