6 problems

Let the internal language of derived $\Gamma$-geometry be the language associated with its $\Gamma$-topoi, and let dependent type theory be extended by a ternary connective modelin…

Let $X_\Gamma$ be a derived $\Gamma$-space, let $\mathcal D_{\mathrm{coh}}(X_\Gamma)$ be its coherent derived category, and let $\mathsf{Phys}_\Gamma$ be the category of $\Gamma$-p…

Let $X$ be a $\Gamma$-scheme, let $\mathbb T_X^\Gamma$ denote its $\Gamma$-tangent $\infty$-category, and let $\mathbb L_X^\Gamma$ denote its cotangent complex. Tangent–cotangent e…

Let $X_{\Gamma}^{\mathrm{nc}}$ be a compact non-commutative derived $\Gamma$-scheme, and let $\mathcal C_\Gamma^{\mathrm{dg}}$ be the dg-category of $\Gamma$-representations. Non-c…

Complexity conjecture. This problem lies in $\mathbf{coNP}$, and becomes $\mathbf{P}$-complete for cyclic additive semirings. The claim gives a proposed complexity classification f…

Let $T$ be a $\Gamma$-semiring and, for each integer $n\geq 3$, let $\mathrm{gldim}^{(n)}_\Gamma(T)$ denote its $n$-ary global dimension. Stability conjecture. For all $n\geq 3$, th…