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Remarks on the stability in arithmetics. (Remarques sur la stabilité en arithmétique.) (French) Zbl 0764.14006

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.

MSC:

14L24 Geometric invariant theory
14L30 Group actions on varieties or schemes (quotients)
13A50 Actions of groups on commutative rings; invariant theory
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