Serre's Conjecture: Finitely generated projective modules over polynomial rings
Abstract
We start by proving that all finitely generated projective R-modules, where R=k[x(1),...,x(n)] and k is a field, are stably free. Then we show that all stably free projective modules over a ring with the unimodular column property are free before showing that the polynomial ring R has the unimodular column property.