Stably free modules of rank 2 over certain real smooth affine threefolds

2025/09/24 by Syed, Tariq
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2509.19699

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.

Citations

• Zero cycles, Mennicke symbols and K₁-stability of certain real affine algebras
• Symplectic orbits of unimodular rows

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