4 problems

Log weak Lefschetz conjecture. Assume that $\mathcal O_Y(E)$ is ample. Then the morphism above is a filtered isomorphism with respect to $P$ if $q\leq d-2$ and strictly injective f…

Weak Lefschetz conjecture. This map is an isomorphism when $2p<\dim(L)$ and is injective modulo torsion when $2p=\dim(L)$. This is the Chow-group analogue of the classical Weak Lef…

Let $X$ be a smooth variety over a field, and let $Y$ be a smooth ample divisor on $X$. Write $\operatorname{CH}^n(X)_\mathbb Q$ and $\operatorname{CH}^n(Y)_\mathbb Q$ for the codi…

Paranjape's weak Lefschetz conjecture. This map is an isomorphism for $p<\dim(Y)/2$. The statement is presented as an analogue of the weak Lefschetz theorem for Chow groups; the so…