Stably free modules of rank $2$ over certain real smooth affine threefolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866912602398916608 |
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| author | Syed, Tariq |
| author_facet | Syed, Tariq |
| contents | Let $R$ be a real smooth affine domain of dimension $3$ such that $R$ has either no real maximal ideals or the intersection of all real maximal ideals in $R$ has height at least $1$. Then we prove that all stably free $R$-modules of rank $2$ are free if and only if the Hermitian $K$-theory group $W_{SL}(R)$ is trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stably free modules of rank $2$ over certain real smooth affine threefolds Syed, Tariq Commutative Algebra Algebraic Geometry K-Theory and Homology Let $R$ be a real smooth affine domain of dimension $3$ such that $R$ has either no real maximal ideals or the intersection of all real maximal ideals in $R$ has height at least $1$. Then we prove that all stably free $R$-modules of rank $2$ are free if and only if the Hermitian $K$-theory group $W_{SL}(R)$ is trivial. |
| title | Stably free modules of rank $2$ over certain real smooth affine threefolds |
| topic | Commutative Algebra Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2509.19699 |