Abstract
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
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Fieker, C. (2006). Applications of the class field theory of global fields. In: Bosma, W., Cannon, J. (eds) Discovering Mathematics with Magma. Algorithms and Computation in Mathematics, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-37634-7_2
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DOI: https://doi.org/10.1007/978-3-540-37634-7_2
Publisher Name: Springer, Berlin, Heidelberg
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