© 2016 American Mathematical Society. For a commutative ring R, we exploit localization techniques and point-free topology to give an explicit realization of both the Zariski frame of R (the frame of radical ideals in R) and its Hochster dual frame as lattices in the poset of localizing subcategories of the unbounded derived category D(R). This yields new conceptual proofs of the classical theorems of Hopkins-Neeman and Thomason. Next we revisit and simplify Balmer’s theory of spectra and supports for tensor triangulated categories from the viewpoint of frames and Hochster duality. Finally we exploit our results to show how a coherent scheme (X, OX) can be reconstructed from the tensor triangulated structure of its derived category of perfect complexes.
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - 1 Jan 2017|
- Hochster duality
- Localizing subcategories
- Reconstruction of schemes
- Triangulated categories
Kock, J., & Pitsch, W. (2017). Hochster duality in derived categories and point-free reconstruction of schemes. Transactions of the American Mathematical Society, 369(1), 223-261. https://doi.org/10.1090/tran/6773