Group actions on algebraic stacks via butterflies

JOURNAL OF ALGEBRA

卷:486

Article

关键词: Algebraic stacks;    Actions on stacks;    2-groups;    Categorical groups;    Weighted projective stacks;    Weighted projective general linear groups;   

DOI  :  10.1016/j.jalgebra.2017.05.002

来源: Elsevier

【 摘 要 】

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 T(n(0), ... , n(r) ), the weighted projective general linear 2-group PGL(n(0), ... , n(r)). As an application, we use a result of ColliotThelene 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). (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free