8 problems

Let $X$ be a smooth connected projective variety of dimension $n$ with CK projectors $\{\pi_i^X\}_{0\leq i\leq 2n}$, and let $\Delta_I^X\in\operatorname{CH}^{mn}(X^{m+1})$ be the…

Let $E$ be an elliptic curve over $\mathbb{Q}$, let $L(E,s)$ be its $L$-function, and let $H^2_{\mathscr{M}}(E,\mathbb{Q}(2))_{\mathbb{Z}}$ denote the integral part of its motivic…

Let $V/\overline{\mathbb Q}$ be a smooth quasiprojective variety. Let … be the Abel–Jacobi map. Bloch–Beilinson conjecture on Abel–Jacobi maps. The map $\Phi_{k,\mathbb Q}$ is inje…

Let $X$ be a smooth projective variety over a number field $k$, let $p$ be a positive integer, and let $F^{\bullet}CH^{p}(X_{\mathbb{C}})_{\mathbb{Q}}$ be the Bloch–Beilinson filtr…

Beilinson's conjecture. The composition

Fully supersingular Bloch--Beilinson conjecture. Numerical and algebraic equivalence coincide on ${\rm CH}^{i}(X)_{\mathbb{Q}}$, so $\operatorname{Griff}^{i}(X)_{\mathbb{Q}}=0$; th…

Voisin's conjecture. For all $l<N$, the anti-symmetrization projector $p_{\wedge^{N+1}}$ acts as zero on $\ker(\operatorname{pr}_*)\otimes\operatorname{CH}_0(S)_{\mathrm{num}}$. Th…

Let $X$ be a smooth projective variety of dimension $n$, and let $L$ be an ample line bundle. Write $A^j_{AJ}(X)_{\Q}$ for the subgroup of Abel–Jacobi trivial codimension-$j$ cycle…