Tags: #open/conjectures 

Statement: every finitely generated [free](free.md);
 
For $k\in \Field$, is every \( M\in \modsleft{\kxn}^\fg \) actually free?
	- True by [Quillen-Suslin](Quillen-Suslin) 76
	
- Open problem ([Bass-Quillen](Bass-Quillen)): 
	- Is the pullback-induced map $\Vect_r(X) \to \Vect_r(X \cross \AA^n)$ a bijection?
	- Proved in special cases