Vol. 1, No. 3, 2016

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The Balmer spectrum of a tame stack

Jack Hall

Vol. 1 (2016), No. 3, 259–274

Let X be a quasicompact algebraic stack with quasifinite and separated diagonal. We classify the thick -ideals of D qc(X)c. If X is tame, then we also compute the Balmer spectrum of the -triangulated category of perfect complexes on X. In addition, if X admits a coarse space X cs, then we prove that the Balmer spectra of X and X cs are naturally isomorphic.

derived categories, algebraic stacks
Mathematical Subject Classification 2010
Primary: 14F05
Secondary: 13D09, 14A20, 18G10
Received: 29 December 2014
Revised: 6 October 2015
Accepted: 4 November 2015
Published: 18 July 2016
Jack Hall
Mathematical Sciences Institute
The Australian National University
Acton ACT 2601