On the cokernel of the Witt decomposition map
Journal de Théorie des Nombres de Bordeaux, Volume 12 (2000) no. 2, pp. 489-501.

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 KG-modules and the one of finite bilinear RG-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.

Soit R un anneau de Dedekind et K son corps de fractions. Soit G un groupe fini. Si R est un anneau d’entiers p-adiques, alors l’application δ de décomposition de Witt entre le groupe de Grothendieck-Witt des KG-modules bilinéaires et celui des RG-modules bilinéaires de torsion est surjective. Pour les corps de nombres K, on démontre que δ est surjective si G est un groupe nilpotent d’ordre impair, et on donne des contre-exemples pour des groupes d’ordre pair.

@article{JTNB_2000__12_2_489_0,
     author = {Nebe, Gabriele},
     title = {On the cokernel of the Witt decomposition map},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {2},
     year = {2000},
     pages = {489-501},
     zbl = {0993.11020},
     mrnumber = {1823199},
     language = {en},
     url={jtnb.centre-mersenne.org/item/JTNB_2000__12_2_489_0/}
}
Nebe, Gabriele. On the cokernel of the Witt decomposition map. Journal de Théorie des Nombres de Bordeaux, Volume 12 (2000) no. 2, pp. 489-501. https://jtnb.centre-mersenne.org/item/JTNB_2000__12_2_489_0/

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