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

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Abstract

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.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé, Université de Lille 1, Cité Scientifique - Bâtiment M2, 59655, Villeneuve d’Ascq Cedex, France

    Ivo Dell’Ambrogio

  2. Fakultät für Mathematik, BIREP Gruppe, Universität Bielefeld,, Postfach 10 01 31, 33501, Bielefeld, Germany

    Greg Stevenson

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  1. Ivo Dell’Ambrogio
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  2. Greg Stevenson
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Correspondence to Ivo Dell’Ambrogio.

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Dell’Ambrogio, I., Stevenson, G. Even More Spectra: Tensor Triangular Comparison Maps via Graded Commutative 2-rings. Appl Categor Struct 22, 169–210 (2014). https://doi.org/10.1007/s10485-012-9296-1

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  • DOI: https://doi.org/10.1007/s10485-012-9296-1

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