Compactification of Reductive Group Schemes
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917277511712768 |
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| author | Nath, Ayan |
| author_facet | Nath, Ayan |
| contents | Let $\mathrm G$ be an isotrivial reductive group over a scheme $S$. We construct a smooth projective $S$-scheme containing $\mathrm G$ as a fiberwise-dense open subscheme equipped with left and right actions of $\mathrm G$ which extend the translation actions of $\mathrm G$ on itself. This verifies a conjecture of Česnavičius (arXiv:2201.06424). When $\mathrm G$ is adjoint, we recover fiberwise the wonderful compactification. Finally, we give an example of a non-isotrivial torus admitting no equivariant compactification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compactification of Reductive Group Schemes Nath, Ayan Algebraic Geometry Let $\mathrm G$ be an isotrivial reductive group over a scheme $S$. We construct a smooth projective $S$-scheme containing $\mathrm G$ as a fiberwise-dense open subscheme equipped with left and right actions of $\mathrm G$ which extend the translation actions of $\mathrm G$ on itself. This verifies a conjecture of Česnavičius (arXiv:2201.06424). When $\mathrm G$ is adjoint, we recover fiberwise the wonderful compactification. Finally, we give an example of a non-isotrivial torus admitting no equivariant compactification. |
| title | Compactification of Reductive Group Schemes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.22462 |