Group actions on algebraic stacks via butterflies
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Volume
486
Pagination
36 - 63
DOI
10.1016/j.jalgebra.2017.05.002
Journal
Journal of Algebra
ISSN
0021-8693
Metadata
Show full item recordAbstract
© 2017 Elsevier Inc.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,⋯,nr) 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 P(n0,⋯,nr), the weighted projective general linear 2-group PGL(n0,⋯,nr). As an application, we use a result of Colliot-Thélène 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,⋯,nr) lifts to a linear action of G on Ar+1.
Authors
Noohi, BCollections
- Mathematics [1468]