Computing the torsion of the $p$-ramified module

Frédéric Pitoun; Firmin Varescon

Computing the torsion of the $p$-ramified module

Number Theory 2013-05-29 v2

Authors: Frédéric Pitoun , Firmin Varescon

Abstract

We fix a prime number $p$ and $\K$ a number field, we denote by $M$ the maximal abelian $p$ -extension of $\Ko$ unramified outside $p$ . The aim of this paper is to study the $\Z_p$ -module $\gal(M/\Ko)$ and to give a method to effectively compute its structure as a $\Z_p$ -module. Then we give numerical results, for real quadratic fields, together with interpretations via Cohen-Lenstra's heuristics.

Cite

@article{arxiv.1302.3099,
  title  = {Computing the torsion of the $p$-ramified module},
  author = {Frédéric Pitoun and Firmin Varescon},
  journal= {arXiv preprint arXiv:1302.3099},
  year   = {2013}
}

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