Group actions on algebraic stacks via butterflies

2007/04/08 by Noohi, Behrang
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0704.1010

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(n₀,...,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(n₀,...,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(n₀,...,n_r) lifts to a linear action of G on A^r+1.

Related

• A note on group actions on algebraic stacks
• Modeling Group Actions on Stacks (Especially the Lubin-Tate Action)
• Stratifying quotient stacks and moduli stacks
• Quotients by non-reductive algebraic group actions
• The étale local structure of algebraic stacks