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Mathematics of Computation

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Computing the torsion of the $ p$-ramified module of a number field

Authors: Frédéric Pitoun and Firmin Varescon
Journal: Math. Comp. 84 (2015), 371-383
MSC (2010): Primary 11R23, 11R37, 11Y40
Published electronically: June 24, 2014
MathSciNet review: 3266966
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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.

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Additional Information

Frédéric Pitoun
Affiliation: 27 Avenue du 8 mai 1945, 11400 Castelnaudary, France

Firmin Varescon
Affiliation: Laboratoire de mathématiques de Besançon, CNRS UMR 6623, Université de Franche Comté, 16 Route de Gray, 25020 Besançon Cédex, France

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
Article copyright: © Copyright 2014 American Mathematical Society

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