# When does the canonical tt-structure restrict to perfect complexes?

I am interested in non-Noetherian(!) rings such that the canonical $$tt$$-structure on $$D(R)D(R)$$ (the derived category of left $$RR$$-modules) restricts to perfect complexes i.e. to the subcategory of complexes of finitely generated projective $$RR$$-modules; i.e., for a complex $$CC$$ of this sort the complex $$…0→Coker(C−1→C0)→C1→C2→…\dots 0\to \operatorname{Coker}(C^{-1}\to C^0)\to C^1\to C^2\to \dots$$ should be quasi-isomorphic to a perfect complex.

This is equivalent to the existence of perfect resolutions for cohomology of perfect complexes. It also appears to be equivalent to the (left) coherence of $$RR$$ (cf. https://mathoverflow.net/a/325943/2191) along with the existence of bounded projective resolutions of all finitely presented $$RR$$-modules. However, I do not know whether the latter assumption is equivalent to the existence of a uniform bound on the length of projective resolutions for arbitrary $$RR$$-modules, i.e., to the finiteness of the left global dimension of $$RR$$. Also, how one can obtain (non-Noetherian) examples? I can certainly take a semi-hereditary $$RR$$, but this is only the “finitely generated” dimension $$11$$ case.

P.S. I also suspect the the ring $$lim→Ri\varinjlim R_i$$ also satisfies my condition if $$RiR_i$$ are of global dimension at most $$nn$$ (where $$nn$$ is fixed) and the transition homomorphisms are flat; is this correct?