论文标题
关于小型科恩·马库拉（Cohen-Macaulay）猜想和最大Cohen-Macaulay模块的新实例的评论
Remarks on the Small Cohen-Macaulay conjecture and new instances of maximal Cohen-Macaulay modules
论文作者
论文摘要
我们表明，任何$ 3 $维的Quasi-Gorenstein Buchsbaum本地戒指的任何准 - 戈伦斯坦的变形，$ i $ invariant $ 1 $承认它是最大的Cohen-Macaulay模块，前提是它是Gorenstein Ring的商。这样一类环包括由Marcel-Schenzel和Imtiaz-Schenzel构建的两个独特分解域的实例。除了这一结果外，还以小型的Cohen-Macaulay猜想为主要特征所激发，我们研究了一个问题，即$ r $ $ -Module $ m $的Frobenius pushforward $ f^e _*（m）$包括最大Cohen-Macaulay在本地和分级的情况下直接达到最大的summand。
We show that any quasi-Gorenstein deformation of a $3$-dimensional quasi-Gorenstein Buchsbaum local ring with $I$-invariant $1$ admits a maximal Cohen-Macaulay module, provided it is a quotient of a Gorenstein ring. Such a class of rings includes two instances of unique factorization domains constructed by Marcel-Schenzel and by Imtiaz-Schenzel, respectively. Apart from this result, motivated by the small Cohen-Macaulay conjecture in prime characteristic, we examine a question about when the Frobenius pushforward $F^e_*(M)$ of an $R$-module $M$ comprises a maximal Cohen-Macaulay direct summand in both local and graded cases.
