3 problems

Let $n\ge1$, let $E_n$ be the $K(n)$-local Lubin–Tate ring spectrum with connective cover $e_n$, and let $\Omega_n$ be the $p$-completed homotopy colimit of the connected commutati…

Let $\Omega_1$ be the $p$-completed homotopy colimit of the connected commutative $\ell_p$-algebras of integers $B$ considered in the source, and let $E_2$ be the $K(2)$-local Lubi…

Let $L_p[1/p]\to M$ be a Galois extension, and let $B$ be a connected commutative $\ell_p$-algebra over $M$ that is semi-finite, or possibly dualizable, as an $\ell_p$-module. Let…