6 problems

Let $X$ be a smooth projective variety, and let $T^pH^l(X;\Q)$ be the topological filtration defined using the natural transformation from morphic cohomology to singular cohomology…

Let $X$ be a smooth projective variety of dimension $m$, let ${\mathbb F}$ be the coefficient field used in the source, and let $\widetilde{L}^tH^k(X;{\mathbb F})$ be the image of…

Let $X$ be a smooth complex projective variety. The cycle class map from morphic cohomology induces a filtration on the singular cohomology of $X$ with rational coefficients, and l…

Cohomological version of Hu's conjecture. If $s<0$, then

Equivariant Suslin's conjecture. This map is an isomorphism for $a\leq 0$ with $a\leq q$ and $b\leq q$, and an injection for $a=1$ with $a\leq q$ and $b\leq q$.

Suslin's conjecture. The comparison morphism above is a quasi-isomorphism on smooth varieties.