On the cohomology groups of local systems over Hilbert modular varieties via Higgs bundles

Stefan Müller-Stach, Mao Sheng, Xuanming Ye +1

Let $X$ be a Hilbert modular variety and $\mathbb{V}$ a non-trivial local system over $X$ with infinite monodromy. In this paper we study Saito's mixed Hodge structure (MHS) on the…