Zuo's arithmetic Higgs bundle conjecture

Let $K$ be a number field, let $(Y,D_Y)$ be a log smooth pair over $K$, and let $(E,\theta)$ be a Higgs bundle over $(Y,D_Y)/K$. The bundle $(E,\theta)$ is arithmetic if there is a positive integer $f$ such that, for almost all finite places $\mathfrak p$ of $K$, its modulo $\mathfrak p$ reduction is a term of a periodic Higgs-de Rham flow whose period is at most $f$; it is motivic in the sense of Zuo's program. Zuo's conjecture. A Higgs bundle over $(Y,D_Y)/K$ is arithmetic if and only if it is motivic. This conjecture seeks to characterize arithmetic Higgs bundles through their geometric or motivic origin and is motivated by Kontsevich's program on the Langlands correspondence. Its status is not determined by the supplied source.