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Quotients of affine spaces by finite groups: from Noether’s problem to Colliot-Thélène conjecture
[2018 KAIST Math. Colloquium]
Date: 2018-10-11
Speaker : Danny Neftin (Technion)
Abstract : Given an action of a finite group G on an affine space A^n, the quotient variety A^n/G have been a subject of interest for over a century, partially motivated by Noether's problem concerning its rationality. Weaker properties of this variety were extensively studied, relating it to the Inverse Galois problem, parametrization of Galois extensions and essential dimension. One of its weakest possible properties, (very) weak approximation, is the subject of a more recent conjecture by Colliot-Th\'el\`ene. We shall discuss the above rationality properties, the conjecture, and the (recent) progress towards it.
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