Recollements of Cohen-Macaulay Auslander algebras and Gorenstein derived categories
Let A, B and C be associative rings with identity. Using a result of Koenig we show that if we have a D b (mod-) level recollement, writing A in terms of B and C, then we get a D (Mod-) level recollement of certain functor categories, induces from the module categories of A, B and C. As an application, we generalise the main theorem of Pan (Sh. Pan, Derived equivalences for Cohen-Macaulay Auslander algebras, J. Pure Appl. Algebra, 216 (2012), 355-363) in terms of recollements of Gorenstein artin algebras. Moreover, we show that being Gorenstein as well as being of finite Cohen-Macaulay type, are invariants with respect to D bp(mod-) level recollements of virtually Gorenstein algebras, where D bp denotes the Gorenstein derived category.