Burnol, Jean-François Remarks on the stability in arithmetics. (Remarques sur la stabilité en arithmétique.) (French) Zbl 0764.14006 Int. Math. Res. Not. 1992, No. 6, 117-127 (1992). The paper gives a metric version for geometric invariant theory over a discretely valued field. The main result states that the distance from the origin of an orbit can be computed from the values of invariant homogeneous polynomials on this orbit. Reviewer: G.Faltings (Princeton) Cited in 1 ReviewCited in 6 Documents MSC: 14L24 Geometric invariant theory 14L30 Group actions on varieties or schemes (quotients) 13A50 Actions of groups on commutative rings; invariant theory Keywords:semistable points; geometric invariant theory PDFBibTeX XMLCite \textit{J.-F. Burnol}, Int. Math. Res. Not. 1992, No. 6, 117--127 (1992; Zbl 0764.14006) Full Text: DOI