Quillen–Suslin theorem
Commutative algebra theorem / From Wikipedia, the free encyclopedia
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"Serre's problem" redirects here. For other uses, see Serre's conjecture (disambiguation).
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 modules and projective modules over polynomial rings. In the geometric setting it is a statement about the triviality of vector bundles on affine space.
Quick Facts Field, Conjectured by ...
Field | Commutative algebra |
---|---|
Conjectured by | Jean-Pierre Serre |
Conjectured in | 1955 |
First proof by | Daniel Quillen Andrei Suslin |
First proof in | 1976 |
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The theorem states that every finitely generated projective module over a polynomial ring is free.