Let R be a ring. We prove that the homotopy category K(R-Proj) is always $\aleph_1$ -compactly
generated, and, depending on the ring R, it may or may not be compactly generated. …

… flat base change morphism, we discuss how understanding these proofs may enable us to
generalize this Grothendieck Duality formula for flat … induced and coinduced module functors i, …

… flat quasi-coherent OX -modules. Where X is affine, we show that this equivalence is the
infinite completion of the Grothendieck duality … the pure derived category of flats and the pure …

… (Alternatively, one can use the Govorov–Lazard characterization of flat modules as filtered
inductive limits of finitely generated projective ones together with the fact that the class of fp-…

… Grothendieck-Verdier dualities, concentrating on such which are related to internal Hom and
coHom functors. Our point of view is the one of module … the simple module S is not flat. The …

… the fundamental class in terms of differential modules, or perhaps cotangent complexes,
via … , where local and global duality merge into a single duality theory, of which fundamental …

… modules on a locally noetherian scheme X are exactly the injective ex-modules which are
quasi-… The most fundamental proper smooth morphism in Grothendieck's approach to duality …

… flat base change, Theorems (4.8.1) and (4.8.3). The abstract theory begins with Theorem (4.1)
(Global Duality… OX-modules such that every lfp OX-module is isomorphic to a member of S. …

… Let us clear up a possible point of confusion: given a scheme X and a complex X of quasi-coherent
sheaves, we say that X is K-flat when it is K-flat as a complex of sheaves of modules …

… category of all OX-modules, and by D(OX) the derived category of all OX-modules. If X is a
… The Grothendieck duality theorem via Bousfield’s techniques and Brown representability. J. …