Corrigendum to "The Brumer-Stark conjecture in some families of extensions of specified degree'' - Institut Camille Jordan Accéder directement au contenu
Article Dans Une Revue Mathematics of Computation Année : 2015

Corrigendum to "The Brumer-Stark conjecture in some families of extensions of specified degree''

Résumé

Barry Smith has found an error in the statement and proof of Lemma 2.5 in our paper [GRT] (Math. Comp. 73 (2004), 297-315). This lemma concerns a cyclic Galois extension K/E of CM fields of odd prime degree p. Towards the end of the proof, it is claimed that every root of unity in E is a norm from K. Our reasoning for this has a gap (the local part of the argument does not work at places where the quadratic extension E/E + is split, where F = E + is the maximal totally real subfield of E), and the statement can indeed fail, as confirmed by a concrete example calculated by Barry Smith. We will first state a corrected version of the lemma, and then we will explain how the proof of Proposition 2.2 has to be adapted. Fortunately, the statement of this proposition (please refer to [GRT]) need not be changed at all, and therefore the rest of the paper is unaffected. (The only other place where Lemma 2.5 is used is in the proof of Proposition 2.1, but there ζ p is not in K, so the relevant case of the lemma is case (i) below, where the formula remains the same.) Lemma 2.5 (revised).

Dates et versions

hal-01657666 , version 1 (17-01-2018)

Identifiants

Citer

Cornelius Greither, Brett Tangedal, Xavier-François Roblot, Xavier-Franç Ois Roblot. Corrigendum to "The Brumer-Stark conjecture in some families of extensions of specified degree''. Mathematics of Computation, 2015, 84, pp.955-957. ⟨10.1090/S0025-5718-2014-02851-2⟩. ⟨hal-01657666⟩
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