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4 results on '"11R70, 11R29"'

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

Author

Jaulent, Jean-François, Pauli, Sebastian, Pohst, Michael, and Soriano-Gafiuk, Florence

Subjects
Mathematics - Number Theory, 11R70, 11R29
Abstract

We present an algorithm for computing the 2-group of the positive divisor classes of a number field F in case F has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel WK2(F) in K2(F) for such number fields.

Published
2008

2. Computation of 2-groups of narrow logarithmic divisor classes of number fields

Author

Jaulent, Jean-François, Pauli, Sebastian, Pohst, Michael, and Soriano-Gafiuk, Florence

Subjects
Mathematics - Number Theory, 11R70, 11R29
Abstract

We present an algorithm for computing the 2-group of narrow logarithmic divisor classes of degree 0 for number fields F. As an application, we compute in some cases the 2-rank of the wild kernel WK2(F).

Published
2008

3. Computation of 2-groups of narrow logarithmic divisor classes of number fields

Author

Jean-François Jaulent, Michael Pohst, Florence Soriano-Gafiuk, Sebastian Pauli, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics and Statistics (DMS), University of North Carolina [Greensboro] (UNCG), University of North Carolina System (UNC)-University of North Carolina System (UNC), Institut für Mathematik [Berlin], Technische Universität Berlin (TU), Laboratoire de Mathématiques et Applications de Metz (LMAM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)

Subjects
Logarithm, Computation, Divisor (algebraic geometry), 01 natural sciences, Wild kernel, Combinatorics, 0502 economics and business, FOS: Mathematics, Number Theory (math.NT), 050207 economics, 0101 mathematics, 11R70 11R29, Mathematics, Discrete mathematics, 11R70, 11R29, Algebra and Number Theory, Mathematics - Number Theory, Degree (graph theory), 010102 general mathematics, 05 social sciences, Algebraic number field, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Computational Mathematics, Logarithmic class group, Narrow logarithmic classes, Kernel (category theory)
Abstract

We present an algorithm for computing the 2-group [email protected][email protected]?"F^r^e^s of narrow logarithmic divisor classes of degree 0 for number fields F. As an application, we compute in some cases the 2-rank of the wild kernel WK"2(F) and the 2-rank of its subgroup K"2^~(F):[email protected]?"n">="1K"2^n(F) of infinite height elements in K"2(F).

Published
2009

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

Author

Jean-François Jaulent, Michael Pohst, Florence Soriano–Gafiuk, Sebastian Pauli, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics and Statistics (DMS), University of North Carolina [Greensboro] (UNCG), University of North Carolina System (UNC)-University of North Carolina System (UNC), Institut für Mathematik [Berlin], Technische Universität Berlin (TU), Laboratoire de Mathématiques et Applications de Metz (LMAM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)

Subjects
11R70, 11R29, Algebra and Number Theory, Kernel (set theory), Mathematics - Number Theory, 010102 general mathematics, 010103 numerical & computational mathematics, Divisor (algebraic geometry), Algebraic number field, 01 natural sciences, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Combinatorics, wild kernel, Number theory, Calculus, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, positive divisor classes, exceptional number fields, 11R70 11R29, Mathematics
Abstract

We present an algorithm for computing the 2-group Cl pos F of the posi- tive divisor classes in case the number field F has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel WK2(F) in K2(F). Resume. Nous developpons un algorithme pour determiner le 2-groupe Cl pos F des classes positives dans le cas ou le corps de nombres considere F possede des places paires exceptionelles. Cela donne en particulier le 2-rang du noyau sauvage WK2(F).

Published
2008
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