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Article Dans Une Revue Glasgow Mathematical Journal Année : 2019

Class number formula for dihedral extensions

Résumé

We give an algebraic proof of a class number formula for dihedral extensions of number fields of degree 2q, where q is any odd integer. Our formula expresses the ratio of class numbers as a ratio of orders of cohomology groups of units and recovers similar formulas which have appeared in the literature as special cases. As a corollary of our main result we obtain explicit bounds on the (finitely many) possible values which can occur as ratio of class numbers in dihedral extensions. Such bounds are obtained by arithmetic means, without resorting to deep integral representation theory.
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Dates et versions

hal-01728713 , version 1 (12-03-2018)

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Luca Caputo, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio. Class number formula for dihedral extensions. Glasgow Mathematical Journal, 2019, ⟨10.1017/S0017089519000144⟩. ⟨hal-01728713⟩
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