  The present note is devoted to an amendment to a recent paper of Ellenberg,
Lawrence and Venkatesh. Roughly speaking, the main result here states the
subpolynomial growth of the number of integral points with bounded height of a
variety over a number field whose fundamental group is large. Such an
improvement, i.e. requiring large fundamental group as opposed to the existence
of a geometric variation of pure Hodge structures, was already asked in
op.cit..
