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Results tagged with algebraic-groups
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user 11682
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.
6
votes
When quotient stacks (for nonsmooth group) are algebraic and related questions
About 1. : no, smoothness isn't essential.
"Flat is enough" : De Jong's slogan to express this result due to M.Artin.
https://www.math.columbia.edu/~dejong/wordpress/?p=1584
I quote :
"Given a flat, f …
- 4,008
5
votes
Are principal bundles isotrivial?
This answer is coming late, but since I have also been struggling to find a reference, I hope this can be helpful to other people.
The answer is yes. Precisely, you can found a proof in
Raynaud, Mi …
- 4,008
4
votes
Does every morphism BG-->BH come from a homomorphism G-->H?
As a complement to the answers above : it is kind of well-known (at least I thought it was) that the natural morphism
$$\operatorname{\mathbf{Hom}}_{gr} (G,H) \to \operatorname{\mathbf{Hom}}(BG,BH)$ …
- 4,008
2
votes
Spin group as an automorphism group
See
Groupes Classiques
Baptiste Calmès, Jean Fasel
http://arxiv.org/abs/1401.1992
Propositions 4.5.1.15 and 4.5.1.16.
- 4,008