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Summary: 2-Gerbes bound by complexes of gr-stacks, and cohomology
Ettore Aldrovandi
Department of Mathematics, Florida State University
Tallahassee, FL 32306-4510, USA
aldrovandi@math.fsu.edu
December 18, 2005
Abstract
We define 2-gerbes bound by complexes of braided group-like stacks. We prove a classification
result in terms of hypercohomology groups with values in abelian crossed squares and cones of
morphisms of complexes of length 3. We give an application to the geometric construction of
certain elements in Hermitian Deligne cohomology groups.
Contents
Introduction 2
1 Background notions 7
1.1 Assumptions and notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Various Deligne complexes and cohomologies . . . . . . . . . . . . . . . . . . . . . 8
2 Gerbes with abelian band 10
2.1 Gerbes bound by a complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Further examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
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