Editing Quillen–Suslin theorem (section)

{{Short description|Commutative algebra theorem}}
{{redirect|Serre's problem|other uses|Serre's conjecture (disambiguation)}}
{{Infobox mathematical statement
| name = Quillen–Suslin theorem
| image = 
| caption = 
| field = [[Commutative algebra]]
| conjectured by = [[Jean-Pierre Serre]]
| conjecture date = 1955
| first proof by = [[Daniel Quillen]]<br>[[Andrei Suslin]]
| first proof date = 1976
}}

The '''Quillen–Suslin theorem''', also known as '''Serre's problem''' or '''Serre's conjecture''', is a [[theorem]] in [[commutative algebra]] concerning the relationship between [[free module]]s and [[projective module]]s over [[polynomial ring]]s. In the geometric setting it is a statement about the triviality of [[vector bundle]]s on [[affine space]].

The theorem states that every [[finitely generated module|finitely generated]] [[projective module]] over a [[polynomial ring]] is [[free module|free]].