4 problems

Hodge realization conjecture. The functor $\iota_{X,\sigma}^{\textup{Hdg}}$ is fully faithful, with essential image stable under subquotients. This is a Hodge-type conjecture for N…

Dynamical model conjecture. There exists an endomorphism $\Phi_C$ such that:

Dynamical realization conjecture. There exists a variety $X$ defined over $\mathbb Q$ and a map $F:X\to X$ such that there is a family of bijections

Let $X$ be a variety, let $M\in\mathcal{ML}(X)$ be a motivic local system, and let $x\in X(\mathbb{C})$. Write $\mathcal{G}_{\textup{mot}}(M,x)$ for the motivic Galois group of $M$…