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