# ag.algebraic geometry – Reductive groups over number rings

Let $$F$$ be a number field.

If $$G$$ is a reductive group over $$mathcal{O}_F$$ then we can look where $$Gotimes mathbb{C}$$ fits in the classification of complex reductive groups and get a “standard model” $$G_{mathrm{st}}$$. The algebraic group $$G$$ will differ from $$G_{mathrm{st}}$$ at only finitely many places.

Is it true that if we fix $$Gotimes mathbb{C}$$ and fix the places of difference then there is only finitely many reductive groups over $$mathcal{O}_F$$ we could have started with?