Quillen–Suslin theorem

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.

"Serre's problem" redirects here. For other uses, see Serre's conjecture (disambiguation).
Quillen–Suslin theorem
FieldCommutative algebra
Conjectured byJean-Pierre Serre
Conjectured in1955
First proof byDaniel Quillen
Andrei Suslin
First proof in1976

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

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