TITLE: Does there exist a projective module over $k[x_1,...,x_n]$ which is not free?
QUESTION [11 upvotes]: I know that finitely generated projective modules over $k[x_1,...,x_n]$ are free does this result hold for any projective module?

Does there exist a projective module over $k[x_1,...,x_n]$ which is not free?

REPLY [4 votes]: A CW answer to remove this from the unanswered list: All projective modules are free; this is the main result of this paper by Hyman Bass.