Higher Direct Images of Coherent Sheaves under a Proper Morphism
نویسنده
چکیده
1.1. Injective resolutions. Let C be an abelian category. An object I ∈ C is injective if the functor Hom(−, I) is exact. An injective resolution of an object A ∈ C is an exact sequence 0→ A→ I → I → . . . where I• are injective. We say C has enough injectives if every object has an injective resolution. It is easy to see that this is equivalent to saying every object can be embedded in an injective object. The following lemma describes the relation between maps of objects and maps of injective resolutions.
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