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Aug 3, 2011 at 17:12 history edited user565739 CC BY-SA 3.0
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Aug 3, 2011 at 0:08 comment added David Roberts Note that the first definition is the quotient in the category of schemes (when it exists) of a group action, and the case when $H$ is a normal sub-group scheme is the cokernel in the category of group schemes. The underlying scheme of the second is the first construction, and using the functor of points, and Yoneda, you should be able to get the group structure on the ordinary quotient in the category of schemes.
Aug 2, 2011 at 13:32 history asked user565739 CC BY-SA 3.0