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- W4300122523 abstract "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-closure and to highlight how it differs from the usual Zariski-closure. When k is perfect, we give a criterion in terms of closed orbits for G to be k-anisotropic, answering a question of Borel." @default.
- W4300122523 created "2022-10-03" @default.
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- W4300122523 date "2014-11-28" @default.
- W4300122523 modified "2023-10-01" @default.
- W4300122523 title "Cocharacter-closure and the rational Hilbert-Mumford Theorem" @default.
- W4300122523 doi "https://doi.org/10.48550/arxiv.1411.7849" @default.
- W4300122523 hasPublicationYear "2014" @default.
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