Cohomology of linking systems with twisted coefficients by a $p$-solvable action
Résumé
In this paper we study the cohomology of the geometric realization of linking systems with coefficients twisted by a $p$-solvable action. More precisely, we try to compare it with the submodule of $\mathcal{F}$-stable elements in the cohomology of the Sylow. The main tools we use is the notion of $p$-local subgroup of index a power of $p$ or prime to $p$. We first study extension by a $p'$-group in a general setting. We give some results for any $p$-solvable action in the case of realizable $p$-local finite groups and make a conjecture that this could be generalized to any $p$-local finite groups. We finally give some constructions and examples to study this conjecture.
Domaines
Mathématiques [math]Origine | Fichiers éditeurs autorisés sur une archive ouverte |
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