Séminaires : Séminaire d'Analyse et Géométrie

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We discuss explicit examples of non-integral variations of Q-Hodge structures. Our approach leverages Fenchel–Nielsen-type parameterizations, due to Kabaya and Maskit, of the Teichmüller component of relative character varieties. Additionally, we discuss various Diophantine results concerning the OK,S -integral points of such character varieties, and give a new proof of Beauville’s classical theorem on families of elliptic curves. If time permits, pathological behaviors of the Hodge locus of non-integral QVHS will also be presented.