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arXiv · 2605.02763

Birational invariance of higher Amitsur groups

Federico Scavia·Yuri Tschinkel·Zhijia Zhang
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Abstract

Let $k$ be a field of characteristic zero and $G$ a finite group. We prove that for all $n\geq 2$, the $n$th Amitsur group is a stable $G$-birational invariant of smooth projective $G$-varieties over $k$. This was previously known for $n=2,3$. For smooth projective $G$-varieties with free and finitely generated Picard group, we also prove that the vanishing of the $G$-equivariant universal torsor obstruction implies the vanishing of the $n$th Amitsur group, for all $n\geq 2$. This was known for $n=2$. Our approach allows for effective computations of these obstructions; we illustrate this with several examples.

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Federico Scavia, Yuri Tschinkel, Zhijia Zhang. 2026-05-04. Birational invariance of higher Amitsur groups. https://arxiv.org/abs/2605.02763

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