On the cokernel of the Witt decomposition map

Gabriele Nebe

Journal de théorie des nombres de Bordeaux (2000)

  • Volume: 12, Issue: 2, page 489-501
  • ISSN: 1246-7405

Abstract

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Let R be a Dedekind domain with field of fractions K and G a finite group. We show that, if R is a ring of p -adic integers, then the Witt decomposition map δ between the Grothendieck-Witt group of bilinear K G -modules and the one of finite bilinear R G -modules is surjective. For number fields K , δ is also surjective, if G is a nilpotent group of odd order, but there are counterexamples for groups of even order.

How to cite

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Nebe, Gabriele. "On the cokernel of the Witt decomposition map." Journal de théorie des nombres de Bordeaux 12.2 (2000): 489-501. <http://eudml.org/doc/248510>.

@article{Nebe2000,
abstract = {Let $R$ be a Dedekind domain with field of fractions $K$ and $G$ a finite group. We show that, if $R$ is a ring of $p$-adic integers, then the Witt decomposition map $\delta $ between the Grothendieck-Witt group of bilinear $KG$-modules and the one of finite bilinear $RG$-modules is surjective. For number fields $K, \delta $ is also surjective, if $G$ is a nilpotent group of odd order, but there are counterexamples for groups of even order.},
author = {Nebe, Gabriele},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Grothendick-Witt group; equivariant Witt group},
language = {eng},
number = {2},
pages = {489-501},
publisher = {Université Bordeaux I},
title = {On the cokernel of the Witt decomposition map},
url = {http://eudml.org/doc/248510},
volume = {12},
year = {2000},
}

TY - JOUR
AU - Nebe, Gabriele
TI - On the cokernel of the Witt decomposition map
JO - Journal de théorie des nombres de Bordeaux
PY - 2000
PB - Université Bordeaux I
VL - 12
IS - 2
SP - 489
EP - 501
AB - Let $R$ be a Dedekind domain with field of fractions $K$ and $G$ a finite group. We show that, if $R$ is a ring of $p$-adic integers, then the Witt decomposition map $\delta $ between the Grothendieck-Witt group of bilinear $KG$-modules and the one of finite bilinear $RG$-modules is surjective. For number fields $K, \delta $ is also surjective, if $G$ is a nilpotent group of odd order, but there are counterexamples for groups of even order.
LA - eng
KW - Grothendick-Witt group; equivariant Witt group
UR - http://eudml.org/doc/248510
ER -

References

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  10. [Rei 75] I. Reiner, Maximal orders. Academic Press (1975). Zbl0305.16001MR1972204
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