3 problems

Period-index conjecture. For every $\alpha in \operatorname{Br}(X)$,

Let $X$ be a smooth cellular $\mathbb{C}$-variety, let $Gr_r$ be the Grassmannian classifying rank-$r$ algebraic bundles, and let $\mathrm{Vect}^{top}(X)$ denote topological vector…

Let $X$ be a smooth projective complex variety and let $m$ be a nonnegative integer. Say that $\operatorname{CH}_0(X)$ is supported on an $m$-dimensional algebraic subset…