5 problems

Voisin's conjecture. Every FK3 should admit a multiplicative Chow–Künneth decomposition.

Strict grading conjecture. This unital grading is a strict grading. More strongly, the graded co-algebra morphism co-induced by the graded split surjection…

A birational Chow–Künneth decomposition of a smooth projective variety is co-multiplicative when the induced grading on its zero-cycles is compatible with the diagonal coproduct. C…

Let $X$ be a holomorphic symplectic variety, let $\operatorname{CH}(X)_{(0)}$ denote the degree-zero part of the Chow grading associated with a Chow--Künneth decomposition, and let…

Let $X$ be an $n$-dimensional connected scheme smooth and projective over ${\bf C}$. Let $M_2(X)^*$ and $i_{2n-2}:M_2(X)^*\otimes {\bf L}^{n-2}\to M(X)$ be as obtained from the dec…