5 problems

Generalized Beilinson and semisimplicity conjecture. The cycle class map induces an isomorphism, and the eigenvalue $1$ of $\operatorname{Frob}_q$ acting on…

Let $X$ be a singular $K3$ surface with Picard rank $20$ over $\mathbb{Q}$, let $H^3_\mathcal{M}(X,\mathbb{Q}(4))_{\operatorname{tr}}$ be the transcendental motivic cohomology, and…

Beilinson's conjecture for higher Chow groups. This map should be injective.

Let $C$ be a smooth projective curve over $\mathbb Q$ of genus $1$, let $E$ be its Jacobian, and let $\alpha$ be a nontrivial element of $H^2_\mathcal M(C,\mathbb Q(3))$. Let…

Soit ${\mathbb F}$ un corps fini et soit $X$ une variété projective et lisse sur ${\mathbb F}$. Pour $i\geq 0$, notons $A^{i}(X)$ le groupe des cycles de codimension $i$ sur $X$ mo…