3 problems

Morel's conjecture. There should be a presentation of the heart of the stable homotopy category $\mathbf{SH}(k)$, equivalently the category of homotopy modules, in terms of a non-o…

Let $k$ be a perfect field. For $n\geq 1$, let $\mathcal{SH}(k)^{{\text{eff}}\heartsuit}$ be the effective heart and $\mathcal{SH}^{S^1}\!(k)(n)^\heartsuit$ the heart of the $n$-th…

Let $M$ be a strictly homotopy invariant sheaf, let $M^{(q)}$ denote its homotopy coniveau tower, and let $\ul{\pi}_0(M^{(q)})$ be the zeroth homotopy sheaf of its $q$-th stage. Co…