Let be a Galois extension with Galois group . We study the set of -linear combinations of characters in the Burnside ring which give rise to -linear combinations of trace forms of subextensions of which are trivial in the Witt ring W of . In particular, we prove that the torsion subgroup of coincides with the kernel of the total signature homomorphism.
Soit une extension galoisienne de groupe de Galois . On étudie l’ensemble des combinaisons linéaires sur de caractères de l’anneau de Burnside , qui induisent des combinaisons -linéaires des formes trace de sous-extensions de qui sont triviales dans l’anneau de Witt W de . On montre que le sous-groupe de torsion de est le noyau de l’homomorphisme signature.
@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}, doi = {10.5802/jtnb.237}, zbl = {0964.11021}, mrnumber = {1730431}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.237/} }
TY - JOUR TI - An analogue of Pfister's local-global principle in the burnside ring JO - Journal de Théorie des Nombres de Bordeaux PY - 1999 DA - 1999/// SP - 31 EP - 44 VL - 11 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.237/ UR - https://zbmath.org/?q=an%3A0964.11021 UR - https://www.ams.org/mathscinet-getitem?mr=1730431 UR - https://doi.org/10.5802/jtnb.237 DO - 10.5802/jtnb.237 LA - en ID - JTNB_1999__11_1_31_0 ER -
Martin Epkenhans. An analogue of Pfister's local-global principle in the burnside ring. Journal de Théorie des Nombres de Bordeaux, Volume 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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