Abstract

It is shown that for any local strongly $F$-regular ring there exists natural number $e_0$ so that if $M$ is any finitely generated maximal Cohen–Macaulay module, then the pushforward of $M$ under the $e_0$th iterate of the Frobenius endomorphism contains a free summand. Consequently, the torsion subgroup of the divisor class group of a local strongly $F$-regular ring is finite.

中文翻译：

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关于最大 Cohen-Macaulay 模的一个定理

摘要

证明对于任何局部强$F$-正则环都存在自然数$e_0$，因此如果$M$是任何有限生成的最大Cohen-Macaulay模，则$M$在$e_0$th下的推进Frobenius 自同态的迭代包含一个自由加数。因此，局部强$F$-正则环的除数类群的扭转子群是有限的。