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5:50 PM
@Denis-CharlesCisinski i see, thanks! i feel like that is at least a little surprising. at least, i don't personally have any good intuition for it.
(and i'd be happy for anyone to share any!)
@Drew thanks for this reference! the statement is for even-periodic commutative ring spectra, but it looks like the proof goes through equally well in the ordinary case of a discrete (complete local regular) ring.
 
 
5 hours later…
10:46 PM
@AaronMazel-Gee Artin-Rees lemma says that, for a complete noetherian ring (with respect to some adic topoogy), there is no difference between completed or discrete tensor product. It also say that any module of finite type is derived complete. If furthermore the ring is regular, then modules of finite type are perfect complexes. Observe then that dualizable objects must be (degreewise) of finite type and bounded.
 

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