论文标题
FreeNESS标准，无需修补本地环上的模块
A freeness criterion without patching for modules over local rings
论文作者
论文摘要
证明，如果$φ\ colon a \ to b $是当地的合法性noetherian本地戒指，那么非零生成的$ b $ b $ -module $ n $，其$ a $的平坦尺寸最多是$ \ mathrm {edim}完整的交叉点。该结果是由泰勒和威尔斯开发的“修补方法”的动机，以及第一作者证明的de smit的猜想，当$ n $超过$ a $时，就处理了特殊情况。
It is proved that if $φ\colon A\to B$ is a local homomorphism of commutative noetherian local rings, a nonzero finitely generated $B$-module $N$ whose flat dimension over $A$ is at most $\mathrm{edim}\, A - \mathrm{edim}\, B$, is free over $B$, and $φ$ is a special type of complete intersection. This result is motivated by a "patching method" developed by Taylor and Wiles, and a conjecture of de Smit, proved by the first author, dealing with the special case when $N$ is flat over $A$.
