Let R be a regular noetherian ring. A central question concerning projective modules over polynomial R-algebras is the following.(1.1) BASS-QUILLEN CONJECTURE ([2] Problem IX, [10]). Every finitely generated projective module P over a polynomial R-algebra R[T], T = (T1,…, Tn) is extended from R, i.e.P≊R[T]⊗R P/(T)P.
A note on D. Quillen’s paper: ‘‘Projective modules over polynomial rings” (Invent. Math. {\bf 36} (1976), 167–171)