6 problems

Let $\mathfrak{M}_{\mathrm{sat}}$ be the category of saturated log motives, let $E$ be a log Tate curve, and let $M$ be an object of $\mathfrak{M}_{\mathrm{sat}}$. Saturated log-mo…

Hodge conjecture for log mixed motives. The realization map is an isomorphism

Second Tate conjecture. The set $\operatorname{Hom}(M,N)$ is in bijection with the set of pairs $(a,b)$ where $a:M_{\ell}\to N_{\ell}$ is a morphism and $b:M_B\to N_B$ is a homomor…

Independence-of-realizations conjecture. Restriction of realizations induces equivalences of categories

Numerical triviality conjecture. In $\mathrm{LM}(S)$, $f\sim g$ implies $f=g$; equivalently,

Logarithmic Chow–Künneth conjecture. The motive $h(X)$ should admit a decomposition