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Rational fixed points for linear group actions

Pietro Corvaja (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove a version of the Hilbert Irreducibility Theorem for linear algebraic groups. Given a connected linear algebraic group G , an affine variety V and a finite map π : V G , all defined over a finitely generated field κ of characteristic zero, Theorem 1.6 provides the natural necessary and sufficient condition under which the set π ( V ( κ ) ) contains a Zariski dense sub-semigroup Γ G ( κ ) ; namely, there must exist an unramified covering p : G ˜ G and a map θ : G ˜ V such that π θ = p . In the case κ = , G = 𝔾 a is the additive group, we reobtain the...

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