Acyclicity of BP-related homologies and cohomologies
\textit{D. Ravenel} [Am. J. Math. 106, 351-414 (1984)] initiated a study of Bousfield classes of Brown-\(Peterson\)-\(related\) spectra. The Bousfield class of the spectrum E, \(<E>\), consists of those spectra F satisfying the following relation for all spectra \(X: F_*X=0\) if and only if \(E_*X=0\). One can also define a cohomology Bousfield class of E, \(<E>^*\), whose members F satisfy the analogous relation: \(F^*X=0\) if and only if \(E^*X=0\). For any p-local spectrum E, there is an Anderson dual spectrum \(\nabla E\) for which \(<\nabla E>^*=<E>\). When does \(<\nabla E>=<E>^* ?\) The author shows that \(<\nabla E>=<E>^*\) if E is one of the friendly Brown-\(Peterson\)-\(related\) spectra \(BP<n>\), E(n), P(n), B(n), and k(n). This equality does not hold for certain infinite products of these spectra.
Bousfield classes of Brown- \(Peterson\)-\(related\) spectra
scientific article; zbMATH DE number 3923671