2 problems

Let $Y$ be a smooth projective variety and let $F$ be a Bloch–Beilinson filtration with rational coefficients on its Chow groups. Assume that $F$ also induces a filtration on Chow…

Let $C$ be a smooth very general curve of genus $g\geq 2k+1$, and let $JC$ be its Jacobian. Write $Z_k$ for the $k$-th Beauville component of the cycle associated with $C$ in…