Please use this identifier to cite or link to this item:
https://dipositint.ub.edu/dspace/handle/2445/35159
Title: | Adams Representability in Triangulated Categories |
Author: | Raventós Morera, Oriol |
Director/Tutor: | Casacuberta, Carles |
Keywords: | Categories abelianes Teoria de l'homotopia Àlgebra homològica Abelian categories Homotopy theory Algebra, Homological |
Issue Date: | 18-Mar-2011 |
Publisher: | Universitat de Barcelona |
Abstract: | [eng] This thesis contains new results about the representability of cohomological functors defined on a subcategory of compact objects (with respect to a fixed cardinal) of a well generated triangulated category. Classical theorems of Adams for the stable homotopy category and Neeman for compactly generated triangulated categories are extended to the first uncountable cardinal. The case of derived categories of rings and the stable motivic category are studied in detail. These results contribute to answering negatively a question raised by Rosický of whether all cohomological functors defined on a subcategory of compact objects with respect to a large enough cardinal are representable. Some of the findings in this thesis are based on new results about abelian categories, the most relevant being a generalization of the Auslander Lemma for non Grothendieck categories. [cat] TESI "Representabilitat d'Adams en categories triangulades" TEXT: En aquesta tesi s'obtenen resultats nous sobre la representabilitat de functors cohomològics definits en subcategories d'objectes compactes (respecte a un cardinal fixat) d'una categoria triangulada ben generada. S'estenen al primer cardinal no numerable teoremes antics d'Adams per a la categoria d'homotopia estable i de Neeman per a categories compactament generades. S'estudien en detall els casos de la categoria derivada d'un anell i la categoria motívica estable. Aquests resultats contribueixen a respondre negativament una pregunta de Rosický sobre si tots els functors cohomològics definits en una subcategoria d'objectes compactes respecte a un cardinal suficientment gran són representables. Alguns dels avenços d'aquesta tesi es basen en nous resultats sobre categories abelianes, el més rellevant dels quals és una generalització del lema d'Auslander per a categories que no són de Grothendieck. |
URI: | http://hdl.handle.net/2445/35159 |
ISBN: | 978-84-694-2874-0 |
Appears in Collections: | Tesis Doctorals - Departament - Algebra i Geometria |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
ORM_THESIS.pdf | 1.03 MB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.