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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.18868 |
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| _version_ | 1866908727299276800 |
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| author | Stavrova, Anastasia |
| author_facet | Stavrova, Anastasia |
| contents | Let $A$ be a regular ring of dimension $\le 2$. Let $G$ be a reductive group over $A$ such that its derived group is a split, i.e. a Chevalley--Demazure, semisimple group. We prove that every Zariski-locally trivial principal $G$-bundle over $A[x_1,\ldots,x_n]$ is extended from $A$, for any $n\ge 1$. This result generalizes to split reductive groups the dimension $2$ case of the Bass--Quillen conjecture on finitely generated projective modules, settled in positive by M. P. Murthy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the generalized Bass--Quillen conjecture in dimension 2 Stavrova, Anastasia Algebraic Geometry K-Theory and Homology Let $A$ be a regular ring of dimension $\le 2$. Let $G$ be a reductive group over $A$ such that its derived group is a split, i.e. a Chevalley--Demazure, semisimple group. We prove that every Zariski-locally trivial principal $G$-bundle over $A[x_1,\ldots,x_n]$ is extended from $A$, for any $n\ge 1$. This result generalizes to split reductive groups the dimension $2$ case of the Bass--Quillen conjecture on finitely generated projective modules, settled in positive by M. P. Murthy. |
| title | On the generalized Bass--Quillen conjecture in dimension 2 |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2512.18868 |