Length 3 Complexes of Abelian Sheaves and Picard 2-Stacks

Details Length 3 Complexes of Abelian Sheaves and Picard 2-Stacks Length 3 Complexes of Abelian Sheaves and Picard 2-Stacks

2009-06-12

arxiv.org/abs/0906.2393v2

Mathematics

Algebraic Geometry

46 pages, the proof of proposition 6.2 is added as appendix

Scientific paper

10.1016/j.aim.2010.06.012

We define a tricategory T of length 3 complexes of abelian sheaves, whose hom-bigroupoids consist of weak morphisms of such complexes. We also define a 3-category 2PIC(S) of Picard 2-stacks, whose hom-2-groupoids consist of additive 2-functors. We prove that these categories are triequivalent as tricategories. As a consequence we obtain a generalization of Deligne's analogous result about Picard stacks in SGA4, Exp. XVIII.

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