4 problems

The spectral Sullivan conjecture. The connective Bousfield class of $L(k)$ is the same as that of some type $k$ finite spectrum.

The height $n$ Telescope Conjecture. The Bousfield class of $T(n)$ agrees with the Bousfield class of $K(n)$:

Let $cKW$ denote connective Witt theory, and let $K(0)$ and $K(w_0)$ be the motivic theories appearing in the source. For a motivic spectrum $E$, write $\langle E\rangle$ for its B…

Let $\mathcal{M}$ be a monoidal model category, let $P$ be an operad, let $L_\mathcal{C}$ be a localization, and let $P_A$ denote the enveloping operad of a $P$-algebra $A$. For…