Extensions of Picard stacks and their homological interpretation

Let S be a site. We introduce the notion of extensions of strictly commutative Picard S-stacks. We define the pull-back, the push-down. and the sum of such extensions and we compute their homological interpretation: if P and Q are two strictly commutative Picard S-stacks, the equivalence classes of extensions of P by Q are parametrized by the cohomology group Ext(1)([P], [Q]), where [P] and [Q] are the complex associated to P and Q respectively. (C) 2011 Elsevier Inc. All rights reserved.