Automorphism 2-group of a weighted projective stack

Behrang Noohi

For a given sequence of positive integers $(n_0,...,n_r)$ we define the {\em weighted projective general linear 2-group} $PGL(n_0,...,n_r)$ as a crossed-module in the category of schemes and show that it is a model for (i.e is naturally homotopy equivalent to) the {\em gr}-stack of self-equivalences of the weighted projective stack of weight $(n_0,...,n_r)$. We also give an explicit description of the structure of $PGL(n_0,...,n_r)$.