43 problems

The Hochschild-to-cyclic spectral sequence for an c4b1c4b7b3bcb1c4b1-algebra $A$ is … Here $A$ is smooth and proper over a field of characteristic $0$. Kontsevich–Soibelman conject…

Tsygan's formality conjecture for chains. Kontsevich's deformation quantization gives an $L_\infty$-quasiisomorphism of $L_\infty$-modules between

Feigin–Losev–Shoikhet's integral conjecture. The FLS-functional satisfies

Let $X$ be a compact smooth space. The modified Hochschild-Kostant-Rosenberg maps $I^K$ and $I_K$ are the maps obtained by twisting the Hochschild-Kostant-Rosenberg isomorphism by…

Let $(X,D)$ and $(X',D')$ be log smooth pairs, and let $E$ be a strong Fourier–Mukai kernel on $X\times^{\log}X'$. Let $\pi:X\times^{\log}X'\to X\times X'$ be the projection and re…

Let $(X,D)$ be a log smooth pair, and let $E_1\to E_2\to E_3\to E_1[1]$ be a distinguished triangle in $D(X\times^{\log}X)$ whose terms are strong log Fourier–Mukai kernels. Additi…

Decategorification isomorphism conjecture. The injective algebra homomorphism above is always an isomorphism.

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 $C:\operatorname{Spec} R\to \mathcal{M}_{cub}$ be a cubic curve, and let $\widehat{C}$ denote its formal completion, a formal group over $R$. Write…

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…

Let $A$ be a nonsmooth $\mathcal{A}_{\infty}$-algebra. Hochschild classes inserted into a categorical enumerative invariant computation, as well as the intermediate classes arising…

Let $\mathcal{T}$ be a smooth proper dg category, and let $\operatorname{Sym}^n\mathcal{T}$ denote its $n$th symmetric power in the sense of Ganter–Kapranov. Write…

The paper considers a quasicompact, quasiseparated, weakly log separated, finite type log algebraic stack $X$, together with its log Hochschild co/homology endofunctors and categor…

Let $K\subset S^3$ be a framed oriented knot and let $X\in\operatorname{Ch}^-(\mathsf{BN}_n)$ be a complex of $n$-strand Bar–Natan 1-morphisms. Let $C(K,V_n)$ denote the $V_n$-colo…

Let $(X,\mathcal{C}^\infty)$ be a homologically regular reduced differentiable space. Let $\mathscr{E}_\bullet(\mathcal{C}^\infty_X)$ be its diagonal sheaf complex and let…

Let $(X,\mathcal{C}^\infty)$ be a homologically regular reduced differentiable stratified space, possibly belonging to an allowable class such as locally semialgebraic differentiab…

Let $G$ be a compact Lie group acting on a manifold $M$, and let $G\ltimes M$ be the associated action groupoid. Write $\mathcal{A}_{G\ltimes M}$ for its convolution algebra and…

Let $M$ be a closed oriented C^-manifold, let $\Omega(M)$ denote its de Rham algebra, and let $\Omega(M)^\vee[-\dim M]$ be the shifted dual complex. Write…

Indecomposability criterion. The category $\mathcal{B}$ is indecomposable if and only if

Let $(\mathscr{V},\otimes,I)$ be a presentably symmetric monoidal $(\infty,1)$-category. Let $\mathscr{M}\mathrm{od}_{\mathscr{V}}$ be the $(\infty,2)$-category whose objects are…

In the special case of enriched categories and bimodules, the relevant objects are spectral categories and their bimodules, with the Hochschild construction providing the expected…

Let $\formalgroup$ be a formal group over a perfect field $k$. For a simplicial commutative $k$-algebra $A$, let $\theta(A)$ be its underlying $E_\infty$-algebra, and write…

Let $\formalgroup$ be a formal group, let $A$ be a simplicial commutative $k$-algebra, and let $\theta(A)$ denote its underlying $E_\infty$-algebra. Write…

Let $\mathfrak g$ be the Lie algebra under consideration, let $s$ denote the degree-sign involution, and let ${{\mathbf A}}_\lambda$ be the corresponding filtered quantization para…

Let $Q$ be the polynomial ring and $f$ a polynomial as in the source, let $n$ be the relevant degree, and let $c_f\in\mathbb{C}$ be the constant such that the canonical pairing on…