3 problems

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

Let $p$ be a prime. Equip the sphere spectrum $\mathbb{S}$ with the trivial $\mathbb{T}$-action, and let … be the canonical cyclotomic structure map. Segal conjecture. The map…

Cyclotomic THH equivalence conjecture. There is an equivalence of cyclotomic spectra