The countable Telescope Conjecture for module categories
| dc.creator | Saroch, Jan | |
| dc.creator | Stovicek, Jan | |
| dc.date | 2008-01-25 | |
| dc.date | 2008-05-16 | |
| dc.date.accessioned | 2026-07-07T10:02:39Z | |
| dc.date.available | 2026-07-07T10:02:39Z | |
| dc.description | By the Telescope Conjecture for Module Categories, we mean the following claim: "Let R be any ring and (A, B) be a hereditary cotorsion pair in Mod-R with A and B closed under direct limits. Then (A, B) is of finite type." We prove a modification of this conjecture with the word 'finite' replaced by 'countable'. We show that a hereditary cotorsion pair (A, B) of modules over an arbitrary ring R is generated by a set of strongly countably presented modules provided that B is closed under unions of well-ordered chains. We also characterize the modules in B and the countably presented modules in A in terms of morphisms between finitely presented modules, and show that (A, B) is cogenerated by a single pure-injective module provided that A is closed under direct limits. Then we move our attention to strong analogies between cotorsion pairs in module categories and localizing pairs in compactly generated triangulated categories. | |
| dc.description | 31 pages; minor changes, typos corrected, references added | |
| dc.identifier | https://arxiv.org/abs/0801.3936 | |
| dc.identifier | http://arxiv.org/abs/0801.3936 | |
| dc.identifier | Adv. Math. 219 (2008) 1002-1036 | |
| dc.identifier | doi:10.1016/j.aim.2008.05.012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169046 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16E30, 18E30 (Primary); 03C60, 16D90, 18G25, 20K40 (Secondary) | |
| dc.title | The countable Telescope Conjecture for module categories | |
| dc.type | text |