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Over an algebraically closed field of characteristic zero, Hacking showed that $\\overline{\\mathcal{M}}_{g,n}$ is rigid (a conjecture of Kapranov). Bruno and Mella for $g=0$, and the second author for $g\\geq 1$ showed that its automorphism group is the symmetric group $S_n$, permuting marked points unless $(g,n)\\in\\{(0,4),(1,1),(1,2)\\}$. The methods used in the papers above do not extend to positive characteristic. 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