38 problems

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…

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…

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…

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…

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…

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…

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…

Let $f:Z\to X$ be a virtual Cartier divisor of derived Artin stacks, and let $\mathcal{F}\in\operatorname{Perf}(Z)$ be a perfect complex of rank $l$. Determinant conjecture. There…

Assume the setting of the derived blow-up $\mathbb{B}l_{Z/X}$ over $S$, with morphism $pr_{Z/X}:\mathbb{B}l_{Z/X}\to X$ and integer $r$ as in the main theorem. Let…

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…

Assumption-free discrepancy and vanishing conjecture. The assumptions that $\mathbb{B}l_f$ is smooth and that $\pi_0(Y)-\pi_0(X)$ is nonempty can be removed from the discrepancy fo…

Analytic non-characteristic derived Cauchy problem. This map is an isomorphism of sheaves of spaces over $Y$. The statement is proposed as a general nonlinear derived Cauchy-Kowale…

Let $X$ be a smooth ambient space, let $f$ define the derived zero locus $\boldsymbol{Z}(f)$, and let $V^{\vee}$ be the ambient dual vector space. The source gives a closed immersi…

Let $\boldsymbol{Y}$ be a quasi-smooth derived scheme, write $Y=t_0(\boldsymbol{Y})$, and let $\widetilde{Y}=t_0(\mathbf{T}^*[-1]\boldsymbol{Y})$. The class…

Let $G$ be the reductive group under consideration, let $\widetilde{G}$ denote its Grothendieck resolution, and let ${\mathcal N}$ be the nilpotent cone in its Lie algebra. Write…

Let $X$ be a smooth projective complex curve. The pro-completed category…