2022-01-28T05:47:54Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000401012021-03-01T21:09:26ZPush-out of SchemesLi, Kezheng138672415application/pdfWe study the existence of a push-out for two morphisms $Z \to X$ and $Z \to Y$ in the category of schemes. Push-out is a generalization of quotient of groupoid. We give a necessary and sufficient condition for the existence of a push-out in the flat projective case. We also give a sufficient condition for the existence of a push-out in the finite normal case, which does not assume any flatness. In particular, this gives a sufficient condition for the existence of a quotient of a finite groupoid on a normal scheme, which does not assume any flatness.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2007-12-28application/pdfJournal of mathematical sciences, the University of Tokyo414531565AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40101/files/jms140403.pdfeng