2 problems

Higher Hodge conjecture. The map $cl_{U}^{p,m}$ is surjective. This is the arithmetic quasiprojective extension of the Hodge conjecture attributed in the source to predictions of B…

Let $U$ be a complex algebraic variety, and let $H_{2i}(U)$ denote its Borel–Moore homology. Define the space of Hodge cycles by … Let $H^{alg}_{2i}(U)$ be the span of the fundamen…