论文标题
小型扰动下的本地同种学
Local cohomology under small perturbations
论文作者
论文摘要
令$（R，\ Mathfrak {M}）$为Noetherian本地戒指，$ i $是$ r $的理想。我们研究了$ \ mathfrak {m} $在小扰动中的$ j $ $ i $的$ j $ change的本地共同体学模块，也就是说，对于理想的$ j $，在$ i $ i $和$ j $ share share smare hillert功能下，$ j $ j $ $ i $ $ $ i $ $ $ i $ $ $ i $ $ $ i $ $ $ i $的$ j $。作为我们的主要结果之一，我们表明，如果$ r/i $是概括性的Cohen-Macaulay，那么$ R/J $的本地共同体模块对于相应的本地同胞学模块$ r/i $是同构的，除非可能是顶级的。特别是，这回答了Quy和V. D. Trung提出的一个问题。我们的方法还使我们可以证明，如果$ r/i $是buchsbaum，那么$ r/j $也是如此。最后，根据一些其他假设，我们表明，如果$ r/i $满足Serre的属性$（s_n）$，那么$ r/j $也是如此。
Let $(R,\mathfrak{m})$ be a Noetherian local ring and $I$ an ideal of $R$. We study how local cohomology modules with support in $\mathfrak{m}$ change for small perturbations $J$ of $I$, that is, for ideals $J$ such that $I\equiv J\bmod \mathfrak{m}^N$ for large $N$, under the hypothesis that $I$ and $J$ share the same Hilbert function. As one of our main results, we show that if $R/I$ is generalized Cohen-Macaulay, then the local cohomology modules of $R/J$ are isomorphic to the corresponding local cohomology modules of $R/I$, except possibly the top one. In particular, this answers a question raised by Quy and V. D. Trung. Our approach also allows us to prove that if $R/I$ is Buchsbaum, then so is $R/J$. Finally, under some additional assumptions, we show that if $R/I$ satisfies Serre's property $(S_n)$, then so does $R/J$.
