{ "id": "2001.00142", "version": "v1", "published": "2020-01-01T05:17:38.000Z", "updated": "2020-01-01T05:17:38.000Z", "title": "The homotopy category of pure injective flats and Grothendieck duality", "authors": [ "Esmaeil Hosseini" ], "comment": "11 pages", "categories": [ "math.AG" ], "abstract": "Let (X;OX) be a locally noetherian scheme with a dualizing complex D. We prove that DOX - : K(PinfX)----> K(InjX) is an equivalence of triangulated categories where K(InjX) is the homotopy category of injective quasi-coherent OX- modules and K(PinfX) is the homotopy category of pure injective flat quasi-coherent OX-modules. Where X is affine, we show that this equivalence is the infinite completion of the Grothendieck duality theorem. Furthermore, we prove that D OX - induces an equivalence between the pure derived category of flats and the pure derived category of absolutely pure quasi-coherent OX-modules.", "revisions": [ { "version": "v1", "updated": "2020-01-01T05:17:38.000Z" } ], "analyses": { "subjects": [ "14F05" ], "keywords": [ "homotopy category", "pure derived category", "pure injective flat quasi-coherent ox-modules", "absolutely pure quasi-coherent ox-modules", "grothendieck duality theorem" ], "note": { "typesetting": "TeX", "pages": 11, "language": "en", "license": "arXiv", "status": "editable" } } }