Let $X$ be a scheme; the fundamental group scheme of $X$, when it
exists, is a profinite group scheme that classifies principal
homogeneous spaces under finite flat group schemes over $X$. We
generalize the construction of the fundamental group scheme given by
M. Nori [No] to the case when $X$ is a reduced flat scheme over a
Dedekind scheme. We prove that if $X$ is a curve over a $p$-adic field
having good reduction, then the prime-to-$p$ part of the fundamental
group scheme of $X$ has only finitely many rational representations in
${\rm GL}\sb N$. In the second part of the paper, using tools from
Arakelov theory, we construct an intrinsic height on the moduli space
of semistable vector bundles (of fixed rank and degree) over a curve
defined over a number field. We finally prove that the height of
vector bundles over an arithmetic surface $X$ coming from
representations of the fundamental group scheme is upper bounded; so
we deduce that there are only finitely many isomorphism classes of
rational representations of the fundamental group scheme of $X$.