要证明最一般的 Bass-Quillen Conjecture， 可以首先解决如下极具启发性的特殊情形：
Question: Let $ (R,\mathfrak{m}) $ be a complete regular local ring which has mixed characteristic $p>0$ and $R$ is unramified (i.e. $ p\notin \mathfrak{m}^{2} $). Then every finite projective $ R[X] $-module is free.