5 problems

Let $X$ be a smooth projective variety of dimension $m$. Assume that $H^{p,q}(X)=0$ for $p\ne q$ and $p<c$ (or $q<c$). Generalized Bloch conjecture. The cycle class map … is inject…

Generalized Bloch conjecture. If $[Z]^*$ vanishes on $H^0(X,\Omega^2_X)$, then $Z_*$ vanishes on $F^2CH_0(X)$.

Let $Y\subset\mathbb{P}^{n}$ be a smooth hypersurface of degree $d$. Write $A_i(Y):=CH_i(Y)_{\mathbb{Q}}$ for the Chow group of $i$-dimensional cycles with rational coefficients mo…

Let $A$ be an abelian variety of dimension $n$. Fix an ample symmetric divisor $D$, set ${\cal C}=D^{n-1}$, and for non-negative integers $j,k,r,d$ define … where $I$ is the augmen…

Bloch's generalized conjecture. For every integer $i\leq c-1$, the cycle map $cl$ is injective. This is presented as a converse to the theorem that injectivity of low-dimensional c…