no. 5
Group Theory
Profinite groups of finite cohomological dimension
[Des groupes profinis de dimension cohomologique finie]

Présenté par : Jean-Pierre Serre

Weigel, Thomas1 ; Zalesskii, Pavel2
1 Università degli studi di Milano-Bicocca, Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi, 8, 20126 Milano, Italy
2 Department of Mathematics, University of Brasilia, 70910-900 Brasilia-DF, Brazil
Comptes Rendus. Mathématique, Tome 338 (2004) no. 5, pp. 353-358.

Soit 1→N→G→G/N→1 une suite exacte courte de groupes profinis, et soit p un nombre premier. Nous montrons que si G a p-dimension cohomologique finie n:=cdp(G) et si l'ordre du groupe H k (N,𝔽 p ) est fini pour k:=cdp(N), la p-dimension cohomologique virtuelle de G/N est égale à n−k.

Let 1→N→G→G/N→1 be a short exact sequence of profinite groups, and let p be a prime number. We prove that if G is of finite cohomological p-dimension n:=cdp(G)<∞ and if the order of H k (N,𝔽 p ) is finite for k:=cdp(N), the virtual cohomological p-dimension of G/N equals n−k.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.12.022
Weigel, Thomas 1 ; Zalesskii, Pavel 2

1 Università degli studi di Milano-Bicocca, Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi, 8, 20126 Milano, Italy
2 Department of Mathematics, University of Brasilia, 70910-900 Brasilia-DF, Brazil 
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Weigel, Thomas; Zalesskii, Pavel. Profinite groups of finite cohomological dimension. Comptes Rendus. Mathématique, Tome 338 (2004) no. 5, pp. 353-358. doi : 10.1016/j.crma.2003.12.022. http://archive.numdam.org/articles/10.1016/j.crma.2003.12.022/

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