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Jan 18, 2021 at 23:16 comment added YCor Thanks for clarifying. Indeed I had the impression that more hypotheses were missing, but it seems indeed to hold in this setting (and "local field" in this book means "nondiscrete locally compact field").
Jan 18, 2021 at 23:12 history edited jaycegetz CC BY-SA 4.0
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Jan 18, 2021 at 23:08 comment added jaycegetz I am confused by this. In the original question the field is local so I didn't say that explicitly before. I don't see how you can't recover the statement I gave above by taking $G=G(F)$, $F=1$, and $\underline{\underline{G}}=G$ in the notation of the reference.
Jan 18, 2021 at 22:49 history edited jaycegetz CC BY-SA 4.0
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Jan 17, 2021 at 12:12 comment added YCor This is far from holding in such a setting. In this theorem there are many assumptions on the field and on the algebraic group which you're omitting.
Jan 17, 2021 at 11:56 history edited YCor CC BY-SA 4.0
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Jan 17, 2021 at 7:56 history answered jaycegetz CC BY-SA 4.0