6 problems

Let $\Theta$ be a tangential structure, let $R$ be its associated ring spectrum, and suppose $\operatorname{Flow}^{\Theta} \simeq \operatorname{Perf}({}_R\operatorname{mod}_R)$. Fo…

Real equivariant conjectures. The six listed assertions in the source hold: the required $\mathbf{E}_{\rho}\rtimes\mathrm{U}(1)_\mathbf{R}$-algebra and splitting structures exist;…

Motivic filtration conjecture. There is a filtration $\mathrm{F}^\star_\mathrm{mot} \mathrm{THH}(R/J(p))$ such that

Conjectural THH computation. There is an isomorphism

The cube decomposition conjecture. The spectrum $\mathrm{THH}(E(n))$ decomposes as a sum of $2^n$ factors: one copy of $E(n)$, together with $2^{n-i-1}$ suspended copies of…

Relative THH conjecture. The relative topological Hochschild homology spectrum should satisfy