\contentsline {section}{\tocsection {}{1}{Introduction}}{1}
\contentsline {subsection}{\tocsubsection {}{1.1}{Rigidified group schemes}}{1}
\contentsline {subsection}{\tocsubsection {}{1.4}{Stable $p$-torsors}}{2}
\contentsline {subsection}{\tocsubsection {}{1.7}{Organization}}{3}
\contentsline {subsection}{\tocsubsection {}{1.8}{Acknowledgements}}{3}
\contentsline {section}{\tocsection {}{2}{The stack $ST_{p,g,h,n}$}}{3}
\contentsline {subsection}{\tocsubsection {}{2.2}{Twisted curves and Log twisted curves}}{3}
\contentsline {subsection}{\tocsubsection {}{2.5}{Proof of proposition\nonbreakingspace 2.1\hbox {}}}{5}
\contentsline {section}{\tocsection {}{3}{Properness}}{6}
\contentsline {section}{\tocsection {}{4}{Examples}}{10}
\contentsline {subsection}{\tocsubsection {}{4.1}{First, some non-examples}}{10}
\contentsline {subsection}{\tocsubsection {}{4.2}{Limit of a $p$-isogeny of elliptic curves}}{10}
\contentsline {subsection}{\tocsubsection {}{4.3}{The double cover of $\mathbb {P}^1$ branched over 4 points}}{11}
\contentsline {section}{\tocsection {Appendix}{A}{Group schemes of order $p$}}{12}
\contentsline {subsection}{\tocsubsection {}{A.4}{Tate-Oort group schemes}}{13}
\contentsline {subsection}{\tocsubsection {}{A.9}{Congruence group schemes}}{14}
\contentsline {subsection}{\tocsubsection {}{A.14}{Equivalence between $TGC$ and $TCG\otimes _\mathbb {Z}\Lambda $}}{17}
\contentsline {subsection}{\tocsubsection {}{A.16}{Proof of theorem\nonbreakingspace A.2\hbox {}}}{19}
\contentsline {section}{\tocsection {Appendix}{B}{Weil restriction of closed subschemes}}{19}
\contentsline {subsection}{\tocsubsection {}{B.1}{Essentially free and pure morphisms}}{20}
\contentsline {subsection}{\tocsubsection {}{B.2}{Representability of $h_*Z$}}{20}
\contentsline {section}{\tocsection {Appendix}{}{References}}{21}