论文标题
取消主要特征多项式环中的射影模块
Cancellation of projective modules in polynomial rings of prime characteristic
论文作者
论文摘要
令$ a $为特征性$ p> 0 $的可交换noetherian戒指，这样$ \ dim（a）= d $。令$ p $为投射$ a [t_1，...，t_n] $ - 等级$ d $的模块。我们表明，只有$ p/p/<t_1，...，t_n> p $是取消的，$ p $是取消的。我们推论一些应用。在一个有趣的后果之一中，我们表明贝斯 - 奎伦（Bass-Quillen）的猜想在第三维度中有一个肯定的答案，当$ 2 $可逆。
Let $A$ be a commutative Noetherian ring of characteristic $p>0$, such that $\dim(A)=d$. Let $P$ be a projective $A[T_1,...,T_n]$-module of rank $d$. We show that $P$ is cancellative if and only if $P/<T_1,...,T_n>P$ is cancellative. We deduce some applications. In one of the interesting consequences, we show that the Bass-Quillen conjecture has an affirmative answer in dimension three, when $2$ is invertible.
