Exact sequences for relative Brauer groups and Picard groups

Abstract

Relative Brauer groups and Picard groups have been introduced in [19] resp. [17]. In both papers we restricted atteention to the Brauer group resp. Picard group of a single couple ( R, σ) consisting of a commutative ring R and an indempotent kernel funktor σ in R-mod. Here we answer the question: what happens to these invariants if we change R or σ? The exact sequences describing this functional behaviour have several applications in ring theory and algebraic geometry, some of which have been included.