Even more spectra: tensor triangular comparison maps via graded commutative 2-rings

Details Even more spectra: tensor triangular comparison maps via graded commutative 2-rings Even more spectra: tensor triangular comparison maps via graded commutative 2-rings

2012-04-10

arxiv.org/abs/1204.2185v1

Mathematics

Category Theory

34 pages, comments welcome

Scientific paper

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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