On stably free modules over affine algebras
Jean Fasel, Richard G. Swan, Ravi A. Rao
TL;DR
This paper proves that under certain conditions, stably free modules of rank d-1 over smooth affine algebras of dimension d are actually free, extending understanding of module structure in algebraic geometry.
Contribution
It establishes a new criterion for the freeness of stably free modules over smooth affine algebras when (d-1)! is invertible in the base field.
Findings
Stably free modules of rank d-1 are free if (d-1)! is nonzero in the base field.
The result applies to smooth affine algebras over algebraically closed fields.
Provides a significant extension of classical results on projective modules.
Abstract
We prove that stably free modules of rank d-1 over a smooth affine algebra of dimension d over an algebraically closed field k are free, provided (d-1)! is nonzero in k.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.