4 problems

Let $K(n)$ be Morava $K$-theory, with periodicity generators $p,v_1,\ldots,v_{n-1}$. Its topological Hochschild cohomology is the spectrum $THH^{\widehat{E(n)}}(K(n))$. Morava K-th…

Let $K(n)$ denote the $2(p^n-1)$-periodic Morava $K$-theory. Its topological Hochschild homology, denoted $THH(K(n))$, may depend a priori on the chosen $A_\infty$ structure. Morav…

Let $R$ be an even commutative $S$-algebra, let $x\in R_d$, and let $p$ be a prime such that $n$ is invertible in $R_*$ for every $n<p$. Let $\bar c_n(x)\in\pi_{p(d+2)-2}R/(p,x)$ d…

Let $R$ be an even commutative $S$-algebra, let $x\in\pi_dR$ be a nonzero divisor, and consider the quotient $R/x$. An $A_\infty$ multiplication is a homotopy-coherent associative…