  The tame fundamental group scheme for an algebraic variety is the maximal
linearly reductive quotient of Nori's fundamental group scheme. In this paper,
we study the tame fundamental group schemes of smooth curves defined over
algebraically closed fields of positive characteristic and develop the theory
of cospecialization maps for them. As a result, we see that the tame
fundamental group schemes heavily depend on the curves. We also see that
numerical invariants of curves can be reconstructed from the tame fundamental
group schemes.
