Nan Gao (Shanghai University)

Compact objects and some adjoints in homotopy categories.

Abstract:

Let A be a CM-finite virtually Gorenstein artin algebra. We prove that the subcategory of compact objects of the homotopy category of Gorenstein-projective modules K(A-GP) admits a duality with the bounded Gorenstein derived category. Let R be a two-sided noetherian ring such that the full subcategory of Gorenstein-flat R-modules is closed under direct products. We show that the inclusion of the homotoy subcategory of Gorenstein-flat modules K(R-GF) into the homotpy category of R-modules K(R-Mod) has a right adjoint, and as an example we show that if X is a locally Gorenstein projective scheme, then the inclusion of K(GF(X)) into K(OcoX) has a right adjoint.