Triangular spectra and their applications to derived categories of noetherian schemes

In recent work, for a triangulated category $\text{cT}$, the author introduced a topological space $\text{tSpec}(\text{cT})$ which we call the triangular spectrum of $\text{cT}$ 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 $\text{dpf}(X)$. 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 $\text{tSpec}(\text{cT})$ and compare the triangular spectrum and the Balmer spectrum as ringed spaces.