Seminar Algebra and Geometry: Arthur Bik (Bern)

Noetherianity up to conjugation

Finite-dimensional vector spaces are Noetherian, i.e. every descending chain of Zariski-closed subsets stabilizes. For infinite-dimensional spaces this is not true. However what can be true is that for some group G acting on the space every descending chain of G-stable closed subsets stablizes. We call spaces for which this holds G-Noetherian. In this talk, we will go over some known examples and non-examples of spaces that are Noetherian up to a group action and introduce some new ones.

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