Computation of 2-groups of positive classes of exceptional number fields

Jean-François Jaulent[1]; Sebastian Pauli[2]; Michael E. Pohst[3]; Florence Soriano–Gafiuk[4]

  • [1] Université de Bordeaux Institut de Mathématiques (IMB) 351, Cours de la Libération 33405 Talence Cedex, France
  • [2] University of North Carolina Department of Mathematics and Statistics Greensboro, NC 27402, USA
  • [3] Technische Universität Berlin Institut für Mathematik MA 8-1 Straße des 17. Juni 136 10623 Berlin, Germany
  • [4] Université Paul Verlaine de Metz LMAM Ile du Saulcy 57000 Metz, France

Journal de Théorie des Nombres de Bordeaux (2008)

  • Volume: 20, Issue: 3, page 715-732
  • ISSN: 1246-7405

Abstract

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We present an algorithm for computing the 2-group 𝒞 ℓ F p o s of the positive divisor classes in case the number field F has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel W K 2 ( F ) in K 2 ( F ) .

How to cite

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Jaulent, Jean-François, et al. "Computation of 2-groups of positive classes of exceptional number fields." Journal de Théorie des Nombres de Bordeaux 20.3 (2008): 715-732. <http://eudml.org/doc/10857>.

@article{Jaulent2008,
abstract = {We present an algorithm for computing the 2-group $\{\mathcal\{C\} \ell \}_F^\{\,pos\}$ of the positive divisor classes in case the number field $F$ has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel $W\!K_2(F)$ in $K_2(F)$.},
affiliation = {Université de Bordeaux Institut de Mathématiques (IMB) 351, Cours de la Libération 33405 Talence Cedex, France; University of North Carolina Department of Mathematics and Statistics Greensboro, NC 27402, USA; Technische Universität Berlin Institut für Mathematik MA 8-1 Straße des 17. Juni 136 10623 Berlin, Germany; Université Paul Verlaine de Metz LMAM Ile du Saulcy 57000 Metz, France},
author = {Jaulent, Jean-François, Pauli, Sebastian, Pohst, Michael E., Soriano–Gafiuk, Florence},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {logarithmic classes; wild kernels},
language = {eng},
number = {3},
pages = {715-732},
publisher = {Université Bordeaux 1},
title = {Computation of 2-groups of positive classes of exceptional number fields},
url = {http://eudml.org/doc/10857},
volume = {20},
year = {2008},
}

TY - JOUR
AU - Jaulent, Jean-François
AU - Pauli, Sebastian
AU - Pohst, Michael E.
AU - Soriano–Gafiuk, Florence
TI - Computation of 2-groups of positive classes of exceptional number fields
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 3
SP - 715
EP - 732
AB - We present an algorithm for computing the 2-group ${\mathcal{C} \ell }_F^{\,pos}$ of the positive divisor classes in case the number field $F$ has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel $W\!K_2(F)$ in $K_2(F)$.
LA - eng
KW - logarithmic classes; wild kernels
UR - http://eudml.org/doc/10857
ER -

References

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  2. J.J. Cannon et al., The computer algebra system Magma, The University of Sydney (2006), http://magma.maths.usyd.edu.au/magma/. 
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  14. J.-F. Jaulent and F. Soriano-Gafiuk, Sur le sous-groupe des éléments de hauteur infinie du K 2 d’un corps de nombres. Acta Arith. 122 (2006), 235–244. Zbl1103.11034MR2239916
  15. S. Pauli and F. Soriano-Gafiuk, The discrete logarithm in logarithmic ℓ -class groups and its applications in K-Theory. In “Algorithmic Number Theory”, D. Buell (ed.), Proceedings of ANTS VI, Springer LNCS 3076 (2004), 367–378. Zbl1125.11354MR2138008
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