The \(Sp_{k,n}\)-local stable homotopy category (Q6091926)

This paper is a generalization of the paper [\textit{M. Hovey} and \textit{N. P. Strickland}, Morava \(K\)-theories and localisation. Providence, RI: American Mathematical Society (AMS) (1999; Zbl 0929.55010)] which studies the categories of \(K(n)\)-local and \(E(n)\)-local spectra. Here \(K(n)\) and \(E(n)\) are the Morava \(K\)-theory and the Johnson-Wilson spectra. Let Sp\(_{k,n}\) denote the full subcategory of the \(\infty\)-category Sp of spectra, consisting of \((K(k)\vee K(k+1)\vee \cdots\vee K(n))\)-local spectra. The categories Sp\(_{n,n}\) and Sp\(_{0,n}\) are the categories of \(K(n)\)-local and \(E(n)\)-local spectra, respectively. The author studies the categories Sp\(_{k,n}\) using a spectrum \(E(n,J_k)\) with Bousfield class \(\langle E(n,J_k)\rangle= \langle K(k)\vee\cdots\vee K(n)\rangle \), in the sections: 2. The category of Sp\(_{k,n}\)-local spectra, 3. Thick subcategories and (co)localizing subcategories, 4. Descent theory and the \(E(n,J_k)\)-local Adams spectral sequence, 5. Dualizable objects in Sp\(_{k,n}\), 6. The Picard group of the Sp\(_{k,n}\)-local category, and 7. \(E(n,J_k)\)-local Brown-Comenetz duality.