Group actions on algebraic stacks via butterflies
Algebraic Geometry
2013-09-06 v2 Quantum Algebra
Abstract
We introduce an explicit method for studying actions of a group stack G on an algebraic stack X. As an example, we study in detail the case where X=P(n_0,...,n_r) is a weighted projective stack over an arbitrary base S. To this end, we give an explicit description of the group stack of automorphisms of, the weighted projective general linear 2-group PGL(n_0,...,n_r). As an application, we use a result of Colliot-Thelene to show that for every linear algebraic group G over an arbitrary base field k (assumed to be reductive if char(k)>0) such that Pic}(G)=0, every action of G on P(n_0,...,n_r) lifts to a linear action of G on A^{r+1}.
Cite
@article{arxiv.0704.1010,
title = {Group actions on algebraic stacks via butterflies},
author = {Behrang Noohi},
journal= {arXiv preprint arXiv:0704.1010},
year = {2013}
}
Comments
Revised version of the preprint previously titled "Automorphism 2-group of a weighted projective stack"