10 problems

Let $X$ and $Y$ be smooth projective varieties of dimension $n$, and let $Z\in CH^n(X\times Y)_{\mathbb Q}$ be a correspondence. Let $F^\bullet$ be the Bloch–Beilinson filtration a…

Self-$K$-isocorrespondence conjecture. If there exists a self-$K$-isocorrespondence $\Sigma\subset X\times X$ passing through an arbitrary pair $(x,y)$, then

Let $X$ be an irreducible smooth projective variety of dimension $n$ over the algebraic closure of a finite field, and let $G_r$ denote the cohomological correspondence of $X$ asso…

Let $X$ be a strict Calabi–Yau manifold of dimension $n$, and let $\omega_X\in H^0(X,K_X)$ be a nowhere-zero top-degree holomorphic form. Let $Z\in CH^n(X\times X)_{\mathbb Q}$ be…

Let $T$) be in a suitable class of correspondences on a compact metric space $(X,d)$, and let $\phi:\mathcal{O}_2(T)\to\mathbb{R}$ be a sufficiently regular function. A transition…

Polynomial relation conjecture. Any Lefschetz cycle satisfies

Nilpotence conjecture. There exists $N>0$ such that

Let $S$ be a smooth projective surface over the field of complex numbers, and let $\Gamma$ be a codimension-two cycle on $S\times S$. The correspondence induces actions $\Gamma^*$…

Standing conjecture. Unitary equivalence of the corresponding correspondences is necessary for the existence of an isomorphism between the relative full crossed products.

Maximal-family correspondence conjecture. Suppose the saturated correspondences with property $\mathcal{S}$ are given only for the maximal members of $\mathcal{L}$, and for every…