10 problems

Let $k$ be a number field, let $\mathbb{V}(k)$ denote the relevant class of varieties over $k$, and let $X\in\mathbb{V}(k)$. The $l$-adic Abel–Jacobi map is the map from the releva…

Let $t\in\mathbb{Q}\setminus\{1\}$, let $X_t$ be the Hesse cubic curve over $\mathbb{Q}$, and let $L(X_t,s)$ be the $L$-function of its first cohomology. The regulator map is … Her…

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 $A$ be an abelian surface over a number field $K$. Write $A_0(A_K)$ for the group of zero-cycles of degree zero on $A_K$, and let $L(H^3(A),s)$ denote the $L$-function of the t…

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 $X$ 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…

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 as in the paper's main theorem, and let $Z:=X/$ be the quotient. Write $A^2_{\mathrm{hom}}(Z)$ for the codimension-two Chow cycles on $Z$ that are homologically trivi…

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…