In the present paper, we study how the scheme-theoretical structure of a curve in positive characteristic explicitly affects the structure of its tame fundamental group. Let \((X_{j}, D_{X_{j}}),\) \(j\in \{1, 2\},\) be a smooth pointed stable curve of type \((g_{X_{j}}, n_{X_{j}})\) over an algebraically closed field \(k_{j}\) of characteristic \(p>0,\) \(U_{X_{j}}{\mathop {=}\limits ^{\textrm{def}}}X_{j}{\setminus } D_{X_{j}},\) and \(\pi _{1}^{\textrm{t}}(U_{X_{j}})\) the tame fundamental group of \((X_{j}, D_{X_{j}}).\) Suppose that \(g_{X_{1}}=0,\) that \(k_{1}{\mathop {=}\limits ^{\textrm{def}}}{\overline{\mathbb {F}}}_{p}\) is an algebraic closure of the finite field \(\mathbb {F}_{p}.\) We give an explicit construction of a finite group G such that G is not a finite quotient of \(\pi _{1}^{\textrm{t}}(U_{X_{1}})\) and is a finite quotient of \(\pi _{1}^{\textrm{t}}(U_{X_{2}})\) if (the minimal models of) \(U_{X_{1}}\) and \(U_{X_{2}}\) are not isomorphic as schemes. As a corollary, our construction deduces a strong generalization of Tamagawa’s results concerning Grothendieck’s anabelian conjecture for curves over algebraically closed fields of characteristic p, namely, the isomorphism classes of smooth pointed stable curves of genus 0 over \({\overline{\mathbb {F}}}_{p}\) can be completely determined not only by using full tame fundamental groups but also by using certain finite quotients of them.
