2 problems

Let $p$ be an odd prime, let $V(1)$ be the Smith–Toda complex, and let $X$ be a type-$2$ atomic spectrum. For a finite $p$-torsion atomic spectrum $X$, define $e(X)=k$ when…

Let $p$ be an odd prime, let $\mathcal C_2$ be the thick subcategory of finite $p$-local spectra of type at least $2$, and let $V(1)$ denote the Smith–Toda complex. Adams's conject…