4 problems

Strict cyclotomic Deligne conjecture. For every natural number $n$, the following diagram of genuine $S^1$-spectra commutes:

For $n\geq 0$ and $p>2$, let $A_*=\operatorname{BP}\langle n\rangle_*[x]/x^e$. Let $w_{n+1,i}$, $y_{j,i}$, and $\gamma_{p^m}(\sigma^2x^e)$ denote the classes introduced in the prec…

Descent spectral sequence surjectivity conjecture. The map

Let $R$ be a discrete ring. Write $Q(R)$ for the spectrum associated with MacLane's $Q$-construction, let $\mathbb{Z}$ denote the Eilenberg–Mac Lane spectrum of the integers, and l…