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Results tagged with algebraic-groups
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user 370
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.
22
votes
3
answers
6k
views
The algebraic fundamental group of a reductive algebraic group
For a connected reductive algebraic group $G$ over a field $k$, other than the \'etale fundamental group of $G$ (regarded just as a scheme), there seems to be another notion, usually called the algebr …
- 4,265
15
votes
Accepted
Is an algebraic space group always a scheme?
I think the answer is yes. If S is a noetherian scheme and G is a relative algebraic group space over S, then there is a stratification of S such that over each stratum, G is a group scheme (see K. Be …
- 4,265
3
votes
How to topologize X(R) when R is a topological ring?
For adelic points of X (or G), one can first topologize X(Q_p) so that it becomes a p-adic analytic variety, and for almost all p one can define an open subset X(Z_p). Then take X(A) to be the restric …
- 4,265
2
votes
algebraic group G vs. algebraic stack BG
Hello Ben,
a little comment: when you say "G is a group scheme over k", you mean k is a separably closed field, right? Because otherwise the groupoid BG(k) may not have only one isomorphism class of …
- 4,265