… Ding injective modules were defined in [13], and they were initially introduced as Gorenstein
… We use \(\mathrm{Hom}(X, Y)\) to present the group of all morphisms from X to Y. Recall that …

… Gorenstein, and we denote its dualising line bundle by . The boundary divisor in a Gorenstein
… to study log smooth morphisms for a fixed underlying morphism has been developed in [40…

In this article a condition is given to detect the containment among thick subcategories of the
bounded derived category of a commutative noetherian ring. More precisely, for a …

… of the proof, as well as deduce a converse ghost lemma whenever the ring has a dualizing
complex. … Then the converse coghost lemma is stated, and a converse ghost lemma is proved. …

… a Q-Gorenstein smoothing to X and D0 = ∂X0 is the toric boundary. … Dualizing, we obtain
a face morphism ση′ … by strata of X with face morphisms, hence gives a generalized cone …

… an object Y is cocompact if the natural morphism … morphism is invertible, so is the left
hand vertical one. Moreover, the left hand vertical morphism is the dual of the natural morphism …

… Evaluation morphisms. We finish this section by giving conditions under which certain natural
evaluation morphisms are isomorphisms. Some of these have appeared elsewhere in the …

… For any flat K-algebra morphism R → R′ with geometrically … Gorenstein. In fact, all rings
we are working with in this chapter are excellent and reduced, hence, approximately Gorenstein…

… K-flat covers exist universally in the category of chain complexes and that the Verdier quotient
of \(K(\mathcal {G})\) by the K-flat … So by the snake lemma, the middle vertical morphism is …

… The morphisms are all morphisms of mixed Hodge structures on the graded pieces of the
perverse Leray filtration; the dotted arrows denote the morphisms induced by composition with …