Opened Access Transfinite Adams representability


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Autor: Muro Jiménez, Fernando
Raventós Morera, Oriol
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2016-04-09
Publicado en: Advances in Mathematics, 292, 111-180.
Tipo de documento: Artículo
Resumen: 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 th...
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Cita: Muro Jiménez, F. y Raventós Morera, O. (2016). Transfinite Adams representability. Advances in Mathematics, 292, 111-180.
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