Timeline for What is the relationship between t-structure and Torsion pair?
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9 events
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| Feb 9, 2010 at 1:11 | comment | added | Greg Stevenson | I'll have to look at some of Rosenberg's preprints. I'd be interested in the connection between t-structures and Bondal-Orlov reconstruction. It has been a while since I looked at the paper but if I understood it and remember it correctly the t-structures were used for studying the autoequivalences. The actual reconstruction only uses the suspended structure and the existence of a Serre functor. | |
| Feb 9, 2010 at 0:58 | comment | added | Shizhuo Zhang | I asked this question to Rosenberg today, he told me that reconstruction theorem for derived category (Bondal-Orlov) is to produce t-structures. I will post this later in this page. | |
| Feb 9, 2010 at 0:57 | comment | added | Shizhuo Zhang | What you mentioned about the hereditary torsion theories are corresponding to the closed subset of injective spectrum is also mentioned in several preprints of Rosenberg but in another language(coreflective categories). He has a spectrum which in general more general than Gabriel spectrum but coincide with it when the category has Gabriel-Krull dimension(in particular, locally noetherian abelian category). | |
| Feb 8, 2010 at 23:27 | history | edited | Greg Stevenson | CC BY-SA 2.5 |
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| Feb 8, 2010 at 14:59 | vote | accept | Shizhuo Zhang | ||
| Feb 8, 2010 at 13:34 | comment | added | Shizhuo Zhang | I will wait for more answers to this question, but your answer is satisfactory enough | |
| Feb 8, 2010 at 13:33 | vote | accept | Shizhuo Zhang | ||
| Feb 8, 2010 at 13:33 | |||||
| Feb 8, 2010 at 13:33 | comment | added | Shizhuo Zhang | Thank you very much. What you mentioned about the injective spectrum can control hereditary torsion theories is interesting! Maybe I will ask a new question about this process | |
| Feb 8, 2010 at 11:32 | history | answered | Greg Stevenson | CC BY-SA 2.5 |