Let R be a commutative Noetherian local ring and M , N be finitely generated R-modules. We
prove a number of results of the form: if Hom R ( M , N ) has some nice properties and Ext R …

… In this section, we obtain various criteria for a module to be free in terms of vanishing of
certain Ext modules and finite projective dimension of certain Hom. We start with the following …

Fix an algebraic space S , and let X and Y be separated Artin stacks of finite presentation over
S with finite diagonals (over S ). We define a stack Hom ̲ S ( X , Y ) classifying morphisms …

… A module over a commutative ring R is called i-realizable if it is isomorphic to Ext i R (B, C)
for suitable R-modules B and C. If R is an integral domain and not a field any torsion-free …

… Ext’s” are part of the Hom-spaces. Moreover, the process of taking the underlying homotopy
category means that we forget these negative Ext’s. In … of Hom-space that we will now turn to. …

… Next we revisit Theorem 1.8 from a slightly different perspective. … Essentially the same proof
as in (1), but with Hom in place of Ext, shows that the given homomorphism N → N2 comes …

… In this chapter we continue with some further investigations, we revisit and generalize the …
In the situation of 3.1.6 and because M is \(\mathfrak {a}\)-separated we also have \({\text {Hom}…

… The point was to cover both Ext and Tor early, and still have enough material for a larger …
We must show that if GE Ab, and if Hom(A & B, G) are given, then there is a unique making …

… Define the Hom-Ext quiver of to be the quiver on vertex set 1,… Hom and Ext of A-modules,
so that undecorated \(\operatorname{Hom}\) and \(\operatorname{Ext}\) can stand for the Hom …

… Hom R ( X , Y ) where X and Y are objects of MF ( R , w ) and MF ( R , w ′ ) , respectively. In
this case, we interpret Hom R ( … The long exact sequence for Ext tells us that Ext • ( M , R ) is …