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تسجيل مستخدم جديدExplicit fibrant replacement for discrete G-spectra
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تأليف
Daniel G. Davis
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If C is the model category of simplicial presheaves on a site with enough points, with fibrations equal to the global fibrations, then it is well-known that the fibrant objects are, in general, mysterious. Thus, it is not surprising that, when G is a profinite group, the fibrant objects in the model category of discrete G-spectra are also difficult to get a handle on. However, with simplicial presheaves, it is possible to construct an explicit fibrant model for an object in C, under certain finiteness conditions. Similarly, in this paper, we show that if G has finite virtual cohomological dimension and X is a discrete G-spectrum, then there is an explicit fibrant model for X. Also, we give several applications of this concrete model related to closed subgroups of G.
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In this thesis we will investigate rational G-spectra for a profinite group G. We will provide an algebraic model for this model category whose injective dimension can be calculated in terms of the Cantor-Bendixson rank of the space of closed subgrou
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