20 problems

Let $E$ be a field of characteristic zero. Let $G$ be a reductive group with Langlands dual group $G^{\vee}$, let $X$ be the underlying curve, and let…

Let $n\geq 0$, let $X$ be a nice enough derived algebraic stack, and let $\widehat{HH}^{E_{n+1}}(X)$ denote its formal higher Hochschild cohomology, so that…

Geometricity conjecture. The derived stack $\mathbb{R}\underline{Vect}_{n}(X)$ of vector bundles on $X$ is geometric.

Full-faithfulness conjecture. The functor $\Theta$ is fully faithful. This would embed the homotopy theory of $DG$-schemes into the homotopy theory of geometric stacks over the mod…

Let $b$ be a symmetric bilinear form and let $\theta_b$ be the holomorphic section of the complex Looijenga line bundle…

Let $\operatorname{Bil}\colon \operatorname{Lat}^{\operatorname{op}}\to\operatorname{AbGroup}\subset\mathrm{PicGrpds}$ be the functor of bilinear forms, and let…

Let $R$ be a commutative ring, and let … be the map classifying the filtered nodal curve over $R$. Denote the corresponding filtered nodal curve by $\mathcal{N}_{\mathrm{fil}}$, an…

Let $C$ be the underlying curve and let $G=\operatorname{GL}_2\times\operatorname{GL}_2$, with Langlands dual group $\check{G}$. Define … whose $R$-points are triples $(F_1,F_2,s)$…

Work in either of the two settings considered in the subsection: the derived analytic or derived algebraic geometric setting with the associated period and Robba rings. Consider pe…

The paper considers formal groups over discrete commutative rings $R$ and the associated categories of formal groups and affine group schemes, together with their Cartier duality.…

A filtered formal group is an abelian cogroup object $A$ in the category of complete filtered algebras $\operatorname{CAlg}(\widehat{\operatorname{Fil}}_R)$ whose underlying algebr…

Triviality conjecture. This derived enhancement is conjectured to be trivial.

Let $F$ be a non-archimedean local field, let $\check G$ be the dual group of a split reductive group, and let $X_{\check G}^{\rm WD}$ be the scheme of $\check G$-valued Weil–Delig…

Let $G$ be an affine algebraic group, and let $\operatorname{LocSys}_G(\overset{\circ}{{\mathcal D}})$ denote the prestack of de Rham $G$-local systems on the punctured formal disc…

The paper considers reduction theorems for Hochschild homology associated with flat $\mathscr{E}$-maps, and notes that analogous algebraic results also have nonflat versions involv…

Monadicity conjecture. If $Z$ is eventually coconnective, then the functor $\iota^{\operatorname{QCoh},!}$ is monadic. The paper states this as a conjectural assertion in the study…

Let $\mathcal{Y}$ be an eventually coconnective quasi-compact algebraic stack locally almost of finite type whose automorphism group at every field-valued point is affine. Passabil…

Let $\mathcal{G}$ be a group-object of $\operatorname{affdgSch}_{\operatorname{aft}}$. Its classifying prestack is $B\mathcal{G}$. The classifying-prestack 1-affineness conjecture.…

Categorified Deligne conjecture. The Drinfeld center $Z(\mathcal C)$ is an $\mathcal E_2$-category.

Natural lift conjecture. The complex $Tr(u)$ has a natural lift