Failure of Weak Approximation in Adjoint Groups
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910133130362880 |
|---|---|
| author | Biswas, Chayansudha |
| author_facet | Biswas, Chayansudha |
| contents | Platonov in 1991 conjectured that adjoint groups are rational as varieties over arbitrary infinite fields, and as a consequence have weak approximation. The rationality part of the conjecture was disproved by Merkurjev in 1996, but the question about weak approximation remained open. We settle this in the negative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14420 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Failure of Weak Approximation in Adjoint Groups Biswas, Chayansudha Algebraic Geometry Rings and Algebras Platonov in 1991 conjectured that adjoint groups are rational as varieties over arbitrary infinite fields, and as a consequence have weak approximation. The rationality part of the conjecture was disproved by Merkurjev in 1996, but the question about weak approximation remained open. We settle this in the negative. |
| title | Failure of Weak Approximation in Adjoint Groups |
| topic | Algebraic Geometry Rings and Algebras |
| url | https://arxiv.org/abs/2604.14420 |