Hello,


I read that if $A\subset D$ is the heart of a bounded t structure, D a triangulated category, then D=D^b(A). 


Have not been able to find a proper reference for this. Can anyone confirm this result?


Thanks!



bounded t structure
You're never going to find a reference because it's false. Just take $D$ to be the stable homotopy category of Postnikov pieces, i.e. spectra with finitely many non-trivial homotopy groups. Take $D\_{\geq 0}$ (resp. $D\_{\leq 0}$) the full subcategory of spectra with non-trivial homotopy groups concentrated in non-negative (resp. non-positive) degrees. This is a $t$-structure whose heart $D\_{\geq 0}\cap D\_{\leq 0}$ is equivalent to the category $Ab$ of abelian groups. There's even a functor $D^b(Ab)\rightarrow D$ preserving the $t$-structure (take the canonical $t$-structure on the left) and inducing an equivalence between the hearts, but $D$ cannot be equivalent to $D^b(Ab)$. Actually $D$ has no algebraic model.


