Suppose X is a smooth algebraic variety (say, in characteristic 0). It’s a folklore result that DbCoh(X) is equivalent to the derived category of complexes of sheaves of OX-modules whose cohomology is coherent. The only reference I could find are these notes, which are written in some exotic language I can’t parse. Does anyone know a more canonical reference?

Maybe a more general question is “what is a general reference to cite when using equivalences between classical (Grothendieck-era) derived categories and their more modern analogues?”

(Lurie’s Higher Algebra will sometimes mention such equivalences without proving them).

**Answer**

**Attribution***Source : Link , Question Author : Dmitry Vaintrob , Answer Author : Community*