The perfect F-locality from the basic F-locality over a Frobenius P-category F

Abstract

Let p be a prime, P a finite p-group, F a Frobenius P-category and F^sc the full subcategory of F over the set of F-selfcentralizing subgroups of P. Recently, we have understood an easy way to obtain the perfect F^sc-locality P^sc from the basic F^sc-locality L^b: it depends on a suitable filtration of the basic F-locality L^b and on a vanishing cohomology result, given with more generality in 'Categorizations of limits of Grothendieck groups over a Frobenius P-category'.