5 problems

Let $X$ be a smooth projective $d$-dimensional variety over $\mathbb{C}$. The cycle class map is … Restrict the target $H^{2k}(X(\mathbb{C}),\mathbb{Z})$ to elements of Hodge type…

The integral Hodge conjecture. $Z^{2i}(X)=0$.

Soit $X$ une variété algébrique complexe projective et lisse, et soit $r$ un entier naturel. La classe de cycle est une application … whose image is contained in…

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 complex projective variety. For any subfield $K\subseteq\mathbb C$, define … and let $H^{\ast,\ast}(X,K)$ be the corresponding graded $K$-algebra. The Hodge con…