On flat generators and Matlis duality for quasicoherent sheaves

Abstract

We show that for a quasicompact quasiseparated schemeX, the following assertions are equivalent: (1) the categoryQCoh(X)of all quasicoherent sheaves onXhas a flat generator; (2) for every injective objectEofQCoh(X), the internal hom functor intoEis exact; (3) the schemeXis semiseparated.

Keywords

• flat
• generators
• Matlis
• duality
• for
• quasicoherent
• sheaves