Discovering Mathematics with Magma

Volume 19 of the series Algorithms and Computation in Mathematics pp 31-62

Applications of the class field theory of global fields

  • Claus FiekerAffiliated withSchool of Mathematics and Statistics, University of Sydney

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Class field theory of global fields provides a description of finite abelian extensions of number fields and of function fields of transcendence degree 1 over finite fields. After a brief review of the handling of both function and number fields in Magma, we give an introduction to computational class field theory focusing on applications: We show how to construct tables of small degree extensions and how to utilize the class field theory to find curves with many rational points.x