It is well known that a picard stack on a site is equivalent to a two term complex of sheaves of abelian groups.
Can we describe the isomorphism classes of gerbes of the picard stack using the two term complex?
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2$\begingroup$ If you consider the complex concentrated in degrees $-1$ and $0$, $\phi:E^{-1}\to E^0$, then probably the group of gerbes is the hypercohomology in degree $1$ of the global sections functor for the complex $E^\bullet$ (degree $1$ rather than $2$, because we already put the kernel of $\phi$ in degree $-1$). $\endgroup$– Jason StarrCommented Feb 22, 2017 at 6:11
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