Birational invariance of higher Amitsur groups
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915978233774080 |
|---|---|
| author | Scavia, Federico Tschinkel, Yuri Zhang, Zhijia |
| author_facet | Scavia, Federico Tschinkel, Yuri Zhang, Zhijia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02763 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Birational invariance of higher Amitsur groups Scavia, Federico Tschinkel, Yuri Zhang, Zhijia Algebraic Geometry 14E08 (Primary) 14M20, 14J50, 20J06 (Secondary) 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. |
| title | Birational invariance of higher Amitsur groups |
| topic | Algebraic Geometry 14E08 (Primary) 14M20, 14J50, 20J06 (Secondary) |
| url | https://arxiv.org/abs/2605.02763 |