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Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.

17 votes

Is an algebraic space group always a scheme?

Let me say first that I am not an algebraic geometer. Nevertheless, in trying to understand the answers to this very question I asked the following question. After hearing the ensuing answers it seems …
Chris Schommer-Pries's user avatar
27 votes
3 answers
3k views

Why is this not an algebraic space?

This question is related to the question Is an algebraic space group always a scheme? which I've just seen which was posted by Anton. His question is whether an algebraic space which is a group object …
Chris Schommer-Pries's user avatar
2 votes
Accepted

Principal bundle for contractible group is weak homotopy equivalence for ind schemes

My recollection is that when you turn these into analytic spaces you get something which is locally contractible topologically. In this case what you are describing is a principal bundle for locally c …
Chris Schommer-Pries's user avatar