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

@article{Epkenhans1999,
abstract = {Let $N/K$ be a Galois extension with Galois group $\mathcal \{G\}$. We study the set $\mathcal \{T\}(\mathcal \{G\})$ of $\mathbb \{Z\}$-linear combinations of characters in the Burnside ring $\mathcal \{B\}(\mathcal \{G\})$ which give rise to $\mathbb \{Z\}$-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 $\mathcal \{B\}(\mathcal \{G\}) / \mathcal \{T\}(\mathcal \{G\})$ coincides with the kernel of the total signature homomorphism.},
author = {Epkenhans, Martin},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {trace forms; Burnside ring; Witt ring},
language = {eng},
number = {1},
pages = {31-44},
publisher = {Université Bordeaux I},
title = {An analogue of Pfister's local-global principle in the burnside ring},
url = {http://eudml.org/doc/248342},
volume = {11},
year = {1999},
}

TY - JOUR
AU - Epkenhans, Martin
TI - An analogue of Pfister's local-global principle in the burnside ring
JO - Journal de théorie des nombres de Bordeaux
PY - 1999
PB - Université Bordeaux I
VL - 11
IS - 1
SP - 31
EP - 44
AB - Let $N/K$ be a Galois extension with Galois group $\mathcal {G}$. We study the set $\mathcal {T}(\mathcal {G})$ of $\mathbb {Z}$-linear combinations of characters in the Burnside ring $\mathcal {B}(\mathcal {G})$ which give rise to $\mathbb {Z}$-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 $\mathcal {B}(\mathcal {G}) / \mathcal {T}(\mathcal {G})$ coincides with the kernel of the total signature homomorphism.
LA - eng
KW - trace forms; Burnside ring; Witt ring
UR - http://eudml.org/doc/248342
ER -