# Approximable triangulated categories

## Seminar/Forum

213
Peter Hall
We will begin the talk with a theorem in algebraic geometry, about the relation between the derived categories $$D^b_{coh}(X)$$ and $$D^{perf}(X)$$ where $$X$$ is a noetherian scheme. The theorem represents a major improvement over what was known.
It turns out that the result is a relatively straightforward corollary of the (somewhat technical) theorem that the category $$D_{qc}(X)$$ is approximable. Approximability is a new notion, a recently introduced useful tool we will explain.