Compactly Generated Triangulated Categories and the Telescope Conjecture
Doctoral thesis
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http://hdl.handle.net/11250/258168Utgivelsesdato
2009Metadata
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Sammendrag
The thesis studies the telescope conjecture for algebraic compactly generated triangulated categories. The conjecture, which says that every smashing localization of a compactly generated triangulated category is generated by compact objects, is answered in affirmative in several cases. Main techniques to achieve this include homological algebra and basic set theoretic methods. At the end, a characterization for homotopy categories of complexes being compactly or, more generally, well generated is given for a wide class of additive categories. Avhandlingen studerer teleskop-formodningen for algebraiske kompaktgenererte triangulerte kategorier. Formodningen, som sier at enhver "smashing" lokalisering av en kompakt generert triangulert kategori, er generert av kompakte objekter, bevises for flere tilfeller. De viktigste teknikkene for å oppnå dette omfatter homologisk algebra og elementære mengdeteoretiske metoder. Til slutt blir en karakterisering av når homotopikategorien av komplekser er, kompakt, eller mer generelt, velgenerert, gitt for en vid klass av additive kategorier.
Består av
Stovicek, Jan. Telescope conjecture, idempotent ideals, andthe trans nite radical. Transactions of the American Mathematical Society. (ISSN 0002-9947). 362: 1475-1489, 2010. 10.1090/S0002-9947-09-04812-0.Krause, Henning; Stovicek, Jan. The telescope conjecture for hereditary ringsvia Ext-orthogonal pairs. .
Jan Stovicek. Locally well generated homotopy categories of complexes. .