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Rationality of the center of a generic division algebra with a group action over a field of characteristic 0
Version 8
(Latest)
June 17, 2026 19:12
Rationality of the center of a generic division algebra with a group action over a field of characteristic 0
Let \(F\) be a field of characteristic \(0\) and let \(H = C_3 \times C_3\) act regularly as a transitive subgroup of \(S_9\). We resolve Problem~5.2 of Auel--Brussel--Garibaldi--Vishne: \(Z_H(F,9)\), the …
Version Notes: Just before submit.
✓ Reviewed
Latest Version
Version 7
June 15, 2026 00:42
Rationality of the center of a generic division algebra with a group action over a field of characteristic 0
Let \(F\) be a field of characteristic \(0\), and let \(H = C_3 \times C_3\) acting regularly as a transitive subgroup of \(S_9\). We study the rationality properties of the …
✓ Reviewed
Version 6
June 14, 2026 23:09
Rationality of the center of a generic division algebra with a group action over a field of characteristic 0
Let \(F\) be a field of characteristic \(0\), and let \(H = C_3 \times C_3\) be a transitive subgroup of \(S_9\). We study the rationality properties of the fixed field …
Version Notes: v6 settles ABGV 5.2 in char 0.
✓ Reviewed
Version 5
June 14, 2026 20:29
Rationality of the center of a generic division algebra with a group action over a field of characteristic 0
Let \(F\) be a field of characteristic \(0\), and let \(H = C_3 \times C_3\) be a transitive subgroup of \(S_9\). We study the rationality properties of the fixed field …
Version Notes: v5. Switching the conclusion to "Not stably rational".
✓ Reviewed
Version 4
June 14, 2026 11:10
Stable rationality of the center of a generic division algebra with a group action over a field of characteristic 0
Let \(F\) be a field of characteristic \(0\) (hence infinite), and let \(H = C_3 \times C_3\) be a transitive subgroup of \(S_9\). We determine the rationality properties of the …
Version Notes: v4
✓ Reviewed
Version 3
June 14, 2026 10:30
Rationality of the center of a generic division algebra with a group action
Let \(F\) be a field of characteristic \(0\) (hence infinite), and let \(H = C_3 \times C_3\) be a transitive subgroup of \(S_9\). We determine the rationality properties of the …
Version Notes: v2. Removed "algebraically closed". The proof of "nonrational" in v1 was wrong.
✓ Reviewed
Version 2
June 14, 2026 10:24
Rationality of the center of a generic division algebra with a group action
Let \(F\) be a field of characteristic \(0\) (hence infinite), and let \(H = C_3 \times C_3\) be a transitive subgroup of \(S_9\). We determine the rationality properties of the …
Version Notes: This is v2. The proof of nonrationality in v1 was wrong.Also, we removed the "algebraically closed" assumption.
✓ Reviewed
Version 1
June 13, 2026 21:49
Rationality of the center of a generic division algebra with a group action
Let \(F\) be an algebraically closed field of characteristic \(0\), and let \(H = C_3 \times C_3\) be a transitive subgroup of \(S_9\). We determine the rationality properties of the …
✓ Reviewed