dc.creator | Muro Jiménez, Fernando | es |
dc.creator | Raventós Morera, Oriol | es |
dc.date.accessioned | 2016-07-04T09:20:54Z | |
dc.date.available | 2016-07-04T09:20:54Z | |
dc.date.issued | 2016-04-09 | |
dc.identifier.citation | Muro Jiménez, F. y Raventós Morera, O. (2016). Transfinite Adams representability. Advances in Mathematics, 292, 111-180. | |
dc.identifier.issn | 0001-8708 | es |
dc.identifier.issn | 1090-2082 | es |
dc.identifier.uri | http://hdl.handle.net/11441/43062 | |
dc.description.abstract | We consider the following problems in a well generated triangulated
category T . Let α be a regular cardinal and T α ⊂ T the full subcategory
of α-compact objects. Is every functor H : (T α) op → Ab that preserves
products of < α objects and takes exact triangles to exact sequences of
the form H ∼= T (−, X)|T α for some X in T ? Is every natural transformation
τ : T (−, X)|T α → T (−, Y )|T α of the form τ = T (−, f)|T α for some
f : X → Y in T ? If the answer to both questions is positive we say that
T satisfies α-Adams representability. A classical result going back to Brown
and Adams shows that the stable homotopy category satisfies ℵ0-Adams representability. The case α = ℵ0 is well understood thanks to the work of Christensen, Keller, and Neeman. In this paper we develop an obstruction theory to decide whether T satisfies α-Adams representability. We derive necessary and sufficient conditions of homological nature, and we compute several examples. In particular, we show that there are rings satisfying α-Adams representability for all α ≥ ℵ0 and rings which do not satisfy α-Adams representability for any α ≥ ℵ0. Moreover, we exhibit rings for which the answer to both questions is no for all ℵω > α ≥ ℵ2. | es |
dc.description.sponsorship | Ministerio de Economía y Competitividad | es |
dc.description.sponsorship | Generalitat de Catalunya | es |
dc.description.sponsorship | Junta de Andalucía | es |
dc.description.sponsorship | German Research Foundation | es |
dc.description.sponsorship | Ministry of Education, Youth and Sports of the Czech Republic | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Advances in Mathematics, 292, 111-180. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | triangulated category | es |
dc.subject | representability | es |
dc.subject | obstruction theory | es |
dc.title | Transfinite Adams representability | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/acceptedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de álgebra | es |
dc.relation.projectID | info:eu-repo/grantAgreement/MINECO/MTM2010-15831 | es |
dc.relation.projectID | info:eu-repo/grantAgreement/MINECO/MTM2013-42178-P | es |
dc.relation.projectID | SGR-119-2009 | es |
dc.relation.projectID | FQM-5713 | es |
dc.relation.projectID | SFB 1085 | es |
dc.relation.projectID | CZ.1.07/2.3.00/20.0003 | es |
dc.identifier.doi | http://dx.doi.org/10.1016/j.aim.2016.01.009 | es |
dc.contributor.group | Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades | es |
idus.format.extent | 58 p. | es |
dc.journaltitle | Advances in Mathematics | es |
dc.publication.volumen | 292 | es |
dc.publication.initialPage | 111 | es |
dc.publication.endPage | 180 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/43062 | |