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.

Soit N/K une extension galoisienne de groupe de Galois 𝒢. On étudie l’ensemble 𝒯(𝒢) des combinaisons linéaires sur de caractères de l’anneau de Burnside (𝒢), qui induisent des combinaisons -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 (𝒢)/𝒯(𝒢) est le noyau de l’homomorphisme signature.

Let N/K be a Galois extension with Galois group 𝒢. We study the set 𝒯(𝒢) of -linear combinations of characters in the Burnside ring (𝒢) which give rise to -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 (𝒢)/𝒯(𝒢) coincides with the kernel of the total signature homomorphism.

@article{JTNB_1999__11_1_31_0,
     author = {Epkenhans, Martin},
     title = {An analogue of {Pfister's} local-global principle in the burnside ring},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {31--44},
     publisher = {Universit\'e Bordeaux I},
     volume = {11},
     number = {1},
     year = {1999},
     doi = {10.5802/jtnb.237},
     zbl = {0964.11021},
     mrnumber = {1730431},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.237/}
}
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. doi : 10.5802/jtnb.237. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.237/

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