66 problems

Let $X$ be a derived critical locus, and let $f$ range over potentials whose derived critical locus is $X$. Derived spectrum equivalence conjecture. The derived spectrum is the sam…

A derived spectrum is the spectrum associated with the derived critical-locus construction of a potential for the moduli space of $\mathop{SL}(2,\mathbb{C})$ representations of a 3…

Let $(X,\mathcal{L},\alpha)$ be an oriented $-1$-shifted contact derived stack over $\mathbb{K}$, and let $\varphi\colon L\to X$ be a proper oriented Legendrian. Write … for the re…

Derived centre conjecture. The functor $\mathbb{R}\operatorname{Center}$ is an idempotent strong monoidal comonad satisfying the Seely isomorphism

Let $X$ be a smooth scheme. Consider the non-linear $\mathcal{D}$-Fredholm index, its symbol complex, and the cycle defined by the associated graded symbol morphism in the total sp…

Cohomological boundedness conjecture. The coherent Springer sheaf $\mathcal{S}$ and each specialization $\mathcal{S}_v$ are honest coherent sheaves; equivalently, their cohomology…

Let the orientation constructed by Joyce and Upmeier be the orientation used to define the motivic Donaldson–Thomas invariants in this paper, and let the orientation used by Behren…

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…

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…

Let $X$ be a Calabi--Yau $3$-fold over a field $k$ of characteristic $p>2$, and let $\operatorname{Map}_{k}(X,\operatorname{\underline{Perf}})$ carry the de Rham $(-1)$-shifted sym…

Derived D-module definitions conjecture. These three definitions yield equivalent symmetric monoidal $\infty$-categories on $X$.

Coisotropic reduction conjecture. The space of $n$-shifted coisotropic structures on $f$ is equivalent to the space of such diagrams, where $\pi_Y$ is an $(n+1)$-shifted Lagrangian…

Lurie–Pridham extension conjecture. The Lurie–Pridham theorem should extend to a theorem relating formal deformation of derived schemes to Lie algebroids over them.

Let $U$ be a smooth $\mathbb{C}$-scheme and let $\phi\colon U\to\mathbb{C}$ be a regular function. Let $\mathbf{M}\to\mathbf{Crit}(\phi)$ be a $(-1)$-shifted Lagrangian such that…

Toën and Vezzosi's conjecture. The assignment from such dg-Lie algebroids to derived foliations is fully faithful.

Let $\mathcal M$ be a derived Hitchin stack, let $\operatorname{Sht}_{\mathcal M}$ be its associated shtuka stack, and let $c_1$ be the correspondence map whose derived dimension i…

Let $X$ be a generalized complex manifold, let $T_X^*\to X$ be its Poisson Lie algebroid, and let $\mathcal{X}=[X/T_X^*]$ be the corresponding quotient stack. The stack…

Let $X$ be a smooth variety, let $V$ be a finite-dimensional complex vector space, and let $\bm{Z}$ be the derived zero locus associated with the function $f$ as in the constructio…

Joyce's conjecture. There is a natural morphism

L-infinity algebroid conjecture. There exists a minimal $L_{\infty}$-algebroid structure on $C_{Z/X}^{\vee}$ whose Chevalley–Eilenberg algebra is equivalent to…

Assume the setting of the derived blow-up $\mathbb{B}l_{Z/X}$ and let $pr_f:\mathbb{B}l_{Z/X}\to X$ be the relevant morphism. Let $\mathfrak{W}_{1-r,1-r}^{f}$ and…

Let $f:X\to Y$ be a morphism between quasi-smooth, locally almost of finite presentation derived Artin stacks. Let $L_{X/Y}$ be the relative cotangent complex and let…