Computational class field theory

2008/02/26 by Cohen, Henri, Stevenhagen, Peter
#11G15 #11R37 #11Y40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0802.3843

Abstract

Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such extensions.

Related

• Notes on abelian class field theory
• Tame Class Field Theory for Global Function Fields
• Class Field Theory and Arithmetic of Abelian Varieties over Local Fields
• On the complexity of class group computations for large degree number fields
• Invitation to higher local fields, Part I, section 16: Higher class field theory without using K-groups