Submission date: 3 October 2019

Abstract:

We consider G, a linear group defined over k, an algebraically closed field. By considering k as an embedded residue field of an algebraically closed valued field K, we can associate to it a compact G-space S^μ_G(k), consisting of μ-types on G. We showed that for each p_μ in S^Dμ_G(k), Stab^μ(p)=Stab(p_μ) is a solvable infinite algebraic group when p_μ is centered at infinity and residually algebraic. Moreover we give a description of the dimension Stab(p_μ) in terms of dimension of p.

Mathematics Subject Classification:

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Full text arXiv 1910.01496: pdf, ps.