19 problems

Generalized Bloch conductor formula. If $p:X\to S$ is an arithmetic $S$-scheme with $S$-proper singular locus $Z$, then

Morsification conjecture for topological exceptional collections. The ordered collection of vanishing cycles obtained from a topological exceptional collection of geometric vanishi…

Let $X$ be a smooth hypersurface and suppose that $n=\dim(X)$ is odd. Let $T_v$ be the connected component of the analytic covering space of the smooth hyperplane-section parameter…

Let $X\subseteq \mathbb P^N$ be a smooth projective variety of dimension $n$, let $Y=X\cap H$ be a smooth hyperplane section, let $U\subseteq (\mathbb P^N)^*$ be the open set of sm…

Let $X$ be a smooth variety over an algebraically closed field $k$ of characteristic $p\neq 2$, let $\mathcal{F}\in D(X)$, and let $(x,\xi)$ be a smooth point of $SS\mathcal{F}$. F…

Let $X$ be a smooth variety over an algebraically closed field $k$ of characteristic $p\neq 2$, and let $\mathcal{F}\in D(X)$. Write $SS\mathcal{F}$ for its singular support and le…

Let $S$ be a strictly henselian trait with closed point $s$, generic point $\eta$, and geometric generic point $\bar\eta$. Let $p:U\to S$ be flat, with $U$ regular and purely of re…

Jacobi-type theorem. There is some positive integer $k$ such that the topological Abel--Jacobi mapping

Strong Tube Theorem. The image of the topological Abel--Jacobi homomorphism

Let $\boldsymbol{Y}$ be a $-2$-shifted symplectic derived scheme over $\operatorname{Spec}{\mathbb C}$, equipped with an orientation, and set $Y=t_0(\boldsymbol{Y})$. Let…

In the situation of the Picard–Lefschetz formula, let $c_1=w_1c_0$ and $c_2=w_2c_0$ with $w_1,w_2\in W$, and let $W_\chi^0$ be the specified subgroup of $W$. Assume that the cosets…

Equality conjecture.

Vanishing-cycle W-algebra action conjecture. There is a $W_\kappa({\mathfrak gl}_r)$-action on this direct sum identifying it with the $W$-vacuum module.

Let $\mathfrak{M}$ be a quasi-smooth QCA derived stack, let $\mathcal{N}=t_0(\Omega_{\mathfrak{M}}[-1])$ be its associated d-critical locus, and let $\mathcal{N}_{\mathrm{st}}$ be…

Let $Q_L^n$ be the Quot schemes associated with the local line $L\subset\mathbb A^3$, and let…

Let $(X,x)$ be the germ under consideration, let $f$ be the defining function, and let $\ell$ be a linear form general enough. Write $\phi_\ell=(\ell,f):(X,x)\to(\mathbb{C}^2,0)$ f…

Let $\mathcal C$ be a $3CY$ triangulated category and let $\mathcal M^{sfr}$ be the moduli space of stable framed objects. Vanishing-cycle conjecture. There is a formal manifold…

Let $Z'$ be a smooth scheme with trivial $\mathbb{G}_m$-action, and let $\mathbb{A}_{\operatorname{\mathbb{C}}}^n$ carry a $\mathbb{G}_m$-action with nonnegative weights. Let…

Let $\Lambda$ be a noetherian torsion ring such that $m\Lambda=0$ for some integer $m$ relatively prime to $p$. Let $S_1$, $S_2$, and $S$ be henselian traits over…