An analogue of Pfister's local-global principle in the burnside ring
Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 31-44

Let N/K be a Galois extension with Galois group 𝒢. We study the set 𝒯(𝒢) of ℤ-linear combinations of characters in the Burnside ring ℬ(𝒢) which give rise to ℤ-linear combinations of trace forms of subextensions of N/K which are trivial in the Witt ring W(K) of K. In particular, we prove that the torsion subgroup of ℬ(𝒢)/𝒯(𝒢) coincides with the kernel of the total signature homomorphism.

Soit N/K une extension galoisienne de groupe de Galois 𝒢. On étudie l’ensemble 𝒯(𝒢) des combinaisons linéaires sur ℤ de caractères de l’anneau de Burnside ℬ(𝒢), qui induisent des combinaisons ℤ-linéaires des formes trace de sous-extensions de N/K qui sont triviales dans l’anneau de Witt W(K) de K. On montre que le sous-groupe de torsion de ℬ(𝒢)/𝒯(𝒢) est le noyau de l’homomorphisme signature.

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     title = {An analogue of {Pfister's} local-global principle in the burnside ring},
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     pages = {31--44},
     year = {1999},
     publisher = {Universit\'e Bordeaux I},
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Martin Epkenhans. An analogue of Pfister's local-global principle in the burnside ring. Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 31-44. https://jtnb.centre-mersenne.org/item/JTNB_1999__11_1_31_0/

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