Applied Categorical Structures

, Volume 22, Issue 1, pp 169–210

Even More Spectra: Tensor Triangular Comparison Maps via Graded Commutative 2-rings



We initiate the theory of graded commutative 2-rings, a categorification of graded commutative rings. The goal is to provide a systematic generalization of Paul Balmer’s comparison maps between the spectrum of tensor-triangulated categories and the Zariski spectra of their central rings. By applying our constructions, we compute the spectrum of the derived category of perfect complexes over any graded commutative ring, and we associate to every scheme with an ample family of line bundles an embedding into the spectrum of an associated graded commutative 2-ring.


Graded ring Symmetric monoidal category Derived category Ample family 

Mathematics Subject Classifications (2010)

13A02 18D10 13D09 


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Laboratoire Paul PainlevéUniversité de Lille 1Villeneuve d’Ascq CedexFrance
  2. 2.Fakultät für Mathematik, BIREP GruppeUniversität Bielefeld,BielefeldGermany

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