5 problems

Let ${\mathcal{O}}$ be a reduced operad in the closed symmetric monoidal category $({\mathsf{Mod}_{\mathcal{R}}},\wedge,{\mathcal{R}})$ of ${\mathcal{R}}$-modules, satisfying the c…

Structured ring spectrum conjecture. The global sections satisfy

Let $\mathcal{O}$ be an operad in $\mathcal{R}$-modules with $\mathcal{O}[0]$ the null object, and factor the canonical map $\mathcal{O}\to\tau_1\mathcal{O}$ as a cofibration follo…

Let $\mathcal{O}$ be an operad, and let $\mathsf{K}$ be the comonad associated to the adjunction comparing $\mathcal{O}$-algebras with $\mathsf{K}$-coalgebras. A homotopy pro-nilpo…

A structured ring-spectrum is called $v_n$-periodic when its algebraic $K$-theory exhibits periodicity detected by the chromatic class $v_n$. For a suitable $v_n$-periodic structur…