9 problems

Sphere–projective-space conjecture. Their Bousfield classes are equal:

X(n)–telescope meet conjecture. For all $n$ and $k$,

X(n)-adjacency conjecture. The spectra $X(n)$ and $X(n+1)$ are adjacent in the Bousfield lattice: if

Bousfield-class dichotomy conjecture. Then

The Dichotomy Conjecture. Every spectrum has either a finite local or a finite acyclic.

Finite detection conjecture for I. If $E\wedge I\neq 0$, then

The decomposition conjecture for D. One has

The minimality conjecture for A(n). If $n\geq 2$, then $\langle A(n)\rangle$ is a minimal nonzero Bousfield class. Moreover, every such $E$ is Bousfield equivalent to a finite wedg…

The quotient-isomorphism conjecture. The epimorphism $r'$ is an isomorphism.