Mathematics > Commutative Algebra
[Submitted on 24 Sep 2025
]
Title: Stably free modules of rank $2$ over certain real smooth affine threefolds
Title: 稳定自由模在某些实光滑仿射三维流形上的秩$2$
Abstract: 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.
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