Extensions of Picard stacks and their homological interpretation

Details Extensions of Picard stacks and their homological interpretation Extensions of Picard stacks and their homological interpretation

2010-03-09

arxiv.org/abs/1003.1866v2

J. of Algebra 331 (2011), no. 1, pp. 28--45

Mathematics

Algebraic Geometry

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Scientific paper

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.

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