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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?

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    $\begingroup$ I think this is a corollary of the Theorem 4.3 from this paper of Bass. $\endgroup$ – user26857 Apr 22 '17 at 16:22
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    $\begingroup$ @spohreis Bass' theorem shows that all projective modules over $k[x_1,...,x_n]$ are free. What do you want more then this? $\endgroup$ – user26857 Oct 11 '17 at 18:40
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    $\begingroup$ Please add this as an answer. $\endgroup$ – spohreis Oct 11 '17 at 20:27
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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.

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    $\begingroup$ According to the paper, shouldn't the answer to the question in the title be 'no'?, i.e. non-f.g. projectives over polynomials rings are free? $\endgroup$ – Pedro Tamaroff Jul 17 '18 at 1:01
  • $\begingroup$ Edited, thanks! $\endgroup$ – David E Speyer Jul 17 '18 at 2:19

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