Tags: #open/conjectures
Statement: every finitely generated free;
For \(k\in \mathsf{Field}\), is every \(M\in {}_{k[x_1, \cdots, x_{n}]}{\mathsf{Mod}}^{\mathrm{fg}}\) actually free? - True by Quillen-Suslin 76
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Open problem (Bass-Quillen):
- Is the pullback-induced map \({ \mathsf{Vect} }_r(X) \to { \mathsf{Vect} }_r(X \times{\mathbf{A}}^n)\) a bijection?
- Proved in special cases