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 Ext1([P],[Q]), where [P] and [Q] are the complex associated to P and Q respectively. © 2011 Elsevier Inc.
Extensions of Picard stacks and their homological interpretation
Bertolin C.
2011
Abstract
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 Ext1([P],[Q]), where [P] and [Q] are the complex associated to P and Q respectively. © 2011 Elsevier Inc.
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