Triangular spectra and their applications to derived categories of noetherian schemes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914014572838912 |
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| author | Matsui, Hiroki |
| author_facet | Matsui, Hiroki |
| contents | In recent work, for a triangulated category $\cT$, the author introduced a topological space $\tSpec(\cT)$ which we call the triangular spectrum of $\cT$ as a tensor-free analog of the Balmer spectrum for a tensor triangulated category. In this paper, we use the triangular spectrum to reconstruct a noetherian scheme $X$ from its perfect derived category $\dpf(X)$. As an application, we give an alternative proof of the Bondal-Orlov-Ballard reconstruction theorem in the special case (when both varieties have ample or anti-ample canonical bundles). Moreover, we define the structure sheaf on $\tSpec(\cT)$ and compare the triangular spectrum and the Balmer spectrum as ringed spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03168 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Triangular spectra and their applications to derived categories of noetherian schemes Matsui, Hiroki Algebraic Geometry Category Theory 14A15, 14F08, 14H52, 18G80 In recent work, for a triangulated category $\cT$, the author introduced a topological space $\tSpec(\cT)$ which we call the triangular spectrum of $\cT$ as a tensor-free analog of the Balmer spectrum for a tensor triangulated category. In this paper, we use the triangular spectrum to reconstruct a noetherian scheme $X$ from its perfect derived category $\dpf(X)$. As an application, we give an alternative proof of the Bondal-Orlov-Ballard reconstruction theorem in the special case (when both varieties have ample or anti-ample canonical bundles). Moreover, we define the structure sheaf on $\tSpec(\cT)$ and compare the triangular spectrum and the Balmer spectrum as ringed spaces. |
| title | Triangular spectra and their applications to derived categories of noetherian schemes |
| topic | Algebraic Geometry Category Theory 14A15, 14F08, 14H52, 18G80 |
| url | https://arxiv.org/abs/2301.03168 |