G-COMPATIBLE TORSION THEORIES - THE SHEAVES PIC(SIGMA) AND B(SIGMA)

When C, D are Grothendieck categories and F : C --> D, G:D --> C are f unctors such that F is exact and F proves G, the extension of torsion theories in D and the restriction of torsion theories in C are defined . In the case that the category C = -(x)-Mod is considered, if sigma l ess than or equal to tau are g(B)-compatible idempotent kernel functor s or with support it is possible to construct an exact sequence of she aves of Brauer and Picard relative groups.