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Preprint Number 23

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23. G. Garkusha and M. Prest
Reconstructing projective schemes from Serre subcategories
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Abstract:

Given a positively graded commutative coherent ring A which is finitely generated as an A_0-algebra, 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 quasi-compact 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

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