Timeline for When does the canonical $t$-structure restrict to perfect complexes?

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Jul 13, 2019 at 13:25	comment	added	user20948		About the global dimension: Proposition 7.2.4.23 in Higher Algebra claims that an almost perfect left module over a connective $\mathbb E_1$-ring is perfect if and only if it has finite $\operatorname{Tor}$-amplitude.
Jul 13, 2019 at 13:09	comment	added	user20948		Maybe almost perfect (sometimes called pseudo-coherent in the literature) instead of perfect is appropriate. On Lurie's Higher Algebra section 7.2.4, especially Proposition 7.2.4.18, he proved that an $\mathbb E_1$-ring $R$ is left coherent if and only if the canonical $t$-structure on the $\infty$-category of left $R$-modules restricts to a $t$-structure on the $\infty$-category of almost perfect left $R$-modules.
Apr 10, 2019 at 15:56	history	edited	Mikhail Bondarko	CC BY-SA 4.0	The P.S. question was added.
Apr 4, 2019 at 16:32	comment	added	Mikhail Bondarko		Yes, it suffices to have bounded projective resolutions of finitely projective modules. and I do not know whether these conditions are equivalent.
Apr 4, 2019 at 11:14	comment	added	Jeremy Rickard		Don't you only need bounded projective resolutions of finitely presented modules, rather than all finitely generated modules?
Apr 4, 2019 at 9:31	history	asked	Mikhail Bondarko	CC BY-SA 4.0