Stability result for projective modules over blowup rings
Abstract
Let R be an affine algebra of dimension n ≥ 3 over an algebraically closed field k. Suppose char k =0 or char k =p ≥ n. Let g,f1,...,fr be a R-regular sequence and A=R[f1/g,...,fr/g]. Let P be a projective A-module of rank n-1 which is extended from R. Let (a,p) ∈ (A P) be a unimodular element and Q=A P/(a,p)A. Then, Q is extended from R. A similar result for affine algebras over reals are also proved.
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