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Sep 2, 2019 at 7:05 vote accept Yoël
Aug 31, 2019 at 21:59 comment added David Loeffler I meant that there is a recipe for describing the fibres at "bad" places $v$. As to whether or not the set $S$ you describe contains all the bad places, I'm not 100% sure, but the Gan--Hanke--Yu paper should give you enough tools to find out.
Aug 31, 2019 at 17:55 comment added Yoël Thank you David for your answer ! Do you mean that GTA's answer - stating that the fiber of $\underline{\mathrm{U}}_V$ at $v$ is reductive whenever $v\notin S$- is a bit too optimistic, but that we might rather enlarge $S$ by adding a finite set of bad primes ?
Aug 31, 2019 at 11:09 history answered David Loeffler CC BY-SA 4.0