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Answer by testaccount for Existence of a regular semisimple element over...

(Edit: the previous version of this answer was not correct, but I leave this here as a remark)Let $\sigma: G \rightarrow G$ be the Frobenius map corresponding to the field automorphism $x \mapsto...

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Answer by Jeff Adler for Existence of a regular semisimple element over...

See Proposition 7.1.4 in Dat, Orlik, and Rapoport, Period domains over finite and $p$-adic fields, Cambridge tracts in Mathematics, vol. 183. While I don't have this book in front of me, I'm pretty...

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Existence of a regular semisimple element over $\mathbb{F}_{q}$

This is probably old, a Chevalley level of old, but I'm not at all an expert in this field so I need help.Let $G$ be a simply connected (almost) simple linear algebraic group defined over...

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