2006.107: The Zariski spectrum of the category of finitely presented modules
2006.107: Mike Prest (2008) The Zariski spectrum of the category of finitely presented modules.
This is the latest version of this eprint.
Full text available as:
 | PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 312 Kb |
Abstract
A representation-theoretic description of the Zariski spectrum of a commutative noetherian ring is applied to more general categories, giving the "Gabriel-Zariski" spectrum. Applied to functor categories it gives a topology, the "rep-Zariski spectrum" on the set of indecomposable pure-injective 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 rep-Zariski spectra are computed. Over commutative coherent rings it is shown that, although its underlying set might be larger, the Gabriel-Zariski 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, pure-injective, Gabriel-Zariski spectrum, rep-Zariski spectrum, Ziegler spectrum, structure sheaf, ring of definable scalars, category of definable scalars, finite type localisation, abelian category, commutative coherent ring. |
| Subjects: | MSC 2000 > 03 Mathematical logic and foundations MSC 2000 > 16 Associative rings and algebras MSC 2000 > 18 Category theory; homological algebra |
| MIMS number: | 2006.107 |
| Deposited By: | Professor Mike Prest |
| Deposited On: | 05 March 2008 |
Available Versions of this Item
- The Zariski spectrum of the category of finitely presented modules (deposited 05 March 2008) [Currently Displayed]
Download Statistics: last 4 weeks
Repository Staff Only: edit this item