No : 1 Title : ‘ Closed Orbits and Uniform S - Instability in Geometric Invariant Theory
نویسندگان
چکیده
In this paper we consider various problems involving the action of a reductive group G on an affine variety V . We prove some general rationality results about the G-orbits in V . In addition, we extend fundamental results of Kempf and Hesselink regarding optimal destabilizing parabolic subgroups of G for such general G-actions. We apply our general rationality results to answer a question of Serre concerning how his notion of G-complete reducibility behaves under separable field extensions. Applications of our new optimality results also include a construction which allows us to associate an optimal destabilizing parabolic subgroup of G to any subgroup of G. Finally, we use these new optimality techniques to provide an answer to Tits’ Centre Conjecture in a special case.
منابع مشابه
No : 6 Title : ‘ Cocharacter - Closure and the Rational Hilbert - Mumford Theorem ’ Author ( S )
For a field k, let G be a reductive k-group and V an affine k-variety on which G acts. Using the notion of cocharacter-closed G(k)-orbits in V , we prove a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant theory. We initiate a study of applications stemming from this rationality tool. A number of examples are discussed to illustrate the concept of cocharacter-...
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