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.
- 20G15, 14L24
- Affine G-variety
- Cocharacter-closed orbit
Bate, M., Herpel, S., Martin, B., & Roehrle, G. (2017). Cocharacter-closure and the rational Hilbert-Mumford Theorem. Mathematische Zeitschrift, 287(1-2), 39-72. https://doi.org/10.1007/s00209-016-1816-5