Prest, Mike (2008) The Zariski spectrum of the category of finitely presented modules. [MIMS Preprint]
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Abstract
A representationtheoretic description of the Zariski spectrum of a commutative noetherian ring is applied to more general categories, giving the "GabrielZariski" spectrum. Applied to functor categories it gives a topology, the "repZariski spectrum" on the set of indecomposable pureinjective modules. This topology is dual to Ziegler's topology on the same underlying set. Associated presheaves of rings and of small abelian categories are defined. Examples of repZariski spectra are computed. Over commutative coherent rings it is shown that, although its underlying set might be larger, the GabrielZariski spectrum is topologically equivalent to the Zariski spectrum.
Item Type:  MIMS Preprint 

Additional Information:  This is the final version of this paper. I expect not to submit this for publication (much of the content will appear elsewhere). 
Uncontrolled Keywords:  Zariski spectrum, injective, pureinjective, GabrielZariski spectrum, repZariski spectrum, Ziegler spectrum, structure sheaf, ring of definable scalars, category of definable scalars, finite type localisation, abelian category, commutative coherent ring. 
Subjects:  MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra 
Depositing User:  Professor Mike Prest 
Date Deposited:  05 Mar 2008 
Last Modified:  08 Nov 2017 18:18 
URI:  http://eprints.maths.manchester.ac.uk/id/eprint/1049 
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The Zariski spectrum of the category of finitely presented modules. (deposited 21 May 2006)
 The Zariski spectrum of the category of finitely presented modules. (deposited 05 Mar 2008) [Currently Displayed]
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