Recollements and localisation theorems
A localisation theorem by A. Neeman states that any recollement of compactly generated triangulated categories induces a short exact sequence of subcategories of compact objects up to direct summands. In this talk, we consider recollements of unbounded derived categories of dg algebras, and we give several localisation theorems with respect to different sub (sub-quotient) categories of the derived categories (e.g. perfect derived categories, perfect valued derived categories, singularity categories, etc.). This is an ongoing joint work with Dong Yang and Guodong Zhou.