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For a triangulated category $\mathcal{T}$, Matsui recently introduced atopological space $\mathrm{Spec}_\triangle(\mathcal{T})$ which we call thetriangular spectrum of $\mathcal{T}$ as an analog of the Balmer spectrumintroduced by Balmer for a tensor triangulated category. In the present paper,we use the triangular spectrum to reconstruct a noetherian scheme $X$ from itsperfect derived category $\mathrm{D^{pf}}(X)$. As an application, we give analternative proof of the Bondal-Orlov-Ballard reconstruction theorem. Moreover,we define the structure sheaf on $\mathrm{Spec}_\triangle(\mathcal{T})$ andcompare the triangular spectrum and the Balmer spectrum as ringed spaces.

Triangular spectra and their applications to derived categories of noetherian schemes