5 problems

Let $Y$ be a smooth projective hyper-Kähler variety, and let $\mathfrak{h}^{\circ}(Y)$ denote its birational motive. Vial's grading conjecture. The birational motive…

Let $X$ be a smooth projective variety whose algebra of holomorphic forms is generated in degrees at most $d$. A birational idempotent correspondence is an idempotent $\varpi$ acti…

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

Let $X$ be a smooth projective variety and let $i$ be a positive integer. Assume that $\mathrm{H}^{*}_{\mathrm{tr}}(X)$ is generated by $\mathrm{H}^i_{\mathrm{tr}}(X)$. Bloch–Beili…

Let $F$ be a field, let $A$ be a coefficient ring, and let $(A,\sim)$ and $(A,\sim')$ be adequate pairs with $A\supseteq \mathbf{Q}$ and $\sim\geq\sim'$. For a motive…