13 problems

Friedlander–Mazur conjecture. For any smooth projective variety $X$ and $k\geq 2p\geq 0$, one has

Let $A$ be an abelian group and let $X$ be a smooth quasi-projective variety of dimension $n$. Let … be the natural transform from Lawson homology to singular homology. Suslin's co…

Hard Lefschetz conjecture for Lawson homology. The map $h^k\bullet$ is injective for $k\geq1$. This conjecture is presented as a Lawson-homology analogue of hard Lefschetz; the sup…

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 $C_{p,d}(\mathbb{P}^n)$ denote the Chow variety of effective algebraic $p$-cycles of degree $d$ in complex projective space, let $L_qH_k(-)_{\mathbb{Q}}$ denote Lawson homology…

Let $\mathrm{SP}^d(\mathbb{P}^n)$ be the $d$-th symmetric product of complex projective space, and let $cl$ denote the cycle class map from Lawson homology to singular homology wit…

Let $C_{p,d}({\mathbb{P}}^n)$ denote the Chow variety of effective $p$-dimensional algebraic cycles of degree $d$ in projective space. Write $\operatorname{Ch}_q$ for the codimensi…

For integers $n\geq p\geq 0$ and $d\geq 0$, let $C_{p,d}({\mathbb{P}}^n)$ denote the Chow variety of effective $p$-dimensional algebraic cycles of degree $d$ in projective space, l…

Teh's conjecture.

Let $A$ be an abelian variety, and write $L_pH_k(A)_{(s)}$ for the eigenspace on which multiplication by $m$ acts with eigenvalue $m^{2g-k-s}$, where $g=\dim A$. Hu's Beauville-typ…

Let $X$ be a high-degree complete intersection variety, and consider the s-maps between its Lawson homology groups. The exceptional indices are those lying in the range covered by…

Let $X$ be a complex smooth projective variety of dimension $d$, and let $L_qH_n(X)$ denote its Lawson homology. Friedlander–Mazur conjecture. For every $q$, one has … for every…

Let $X$ be a complex smooth projective variety. For integers $q$ and $n$, let $L_qH_n(X)$ denote Lawson homology and let $H_n(X^{an})$ denote the singular homology of the analytic…