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Timeline for Definition of abelian variety

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Sep 10, 2011 at 12:21 vote accept Descartes
Sep 10, 2011 at 11:40 comment added user2035 In a scheme which is locally of finite type over a field, the set of closed points is dense. In the reasoning above, we only know that the equalizer is reduced after we have concluded that it equals $A$.
Sep 10, 2011 at 11:22 comment added Descartes Sorry, the question in the comment became clear to me somewhat afterwards. But just one last thing: a closed subscheme which contains all closed points is the whole space? And why is the equalizer reduced? Thank you!
Sep 10, 2011 at 10:48 comment added user2035 The preceding comment was an answer to a comment which has now disappeared.
Sep 10, 2011 at 10:39 comment added user2035 The group axioms all have the form $f=g$ as in the second paragraph, so can be checked on $\bar k$-valued points.
Sep 10, 2011 at 10:28 history answered user2035 CC BY-SA 3.0