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Preprint Number 23
23. G. Garkusha and M. Prest Reconstructing projective schemes from Serre subcategories Email: Submission date: Abstract: Given a positively graded commutative coherent ring A which is finitely generated as an A_0algebra, a bijection between the tensor Serre subcategories of {\rm qgr}(A) and the set of all subsets of {\rm Proj}(A) which are unions of sets with quasicompact open complement is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of isomorphism classes of indecomposable injective graded modules are used in an essential way. There is, also constructed an isomorphism of associated ringed spaces. Mathematics Subject Classification: 03, 14, 16, 18 Keywords and phrases: commutative graded ring, finitely presented module, torsion module, injective module, projective scheme, Zariski topology Full text: pdf.

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