An analogue of Pfister's local-global principle in the burnside ring

Martin Epkenhans

Martin Epkenhans

Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 31-44.

Résumé
Abstract

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.

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.

MR Zbl

@article{JTNB_1999__11_1_31_0,
     author = {Martin Epkenhans},
     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},
     zbl = {0964.11021},
     mrnumber = {1730431},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1999__11_1_31_0/}
}

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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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