发表机构
Kharazmi University（卡拉兹米大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在交换Noether环框架下，通过双复形与谱序列，证明了关于Serre子范畴的上同调模包含关系的一个蕴含结论。
AI 中文摘要
设R为交换Noether环，x=x₁,…,xₙ为R-正则序列，y=y₁,…,yₘ为R的元素序列，记I=(y)，S为R模范畴的Serre子范畴。考虑由关于x的Koszul上复形与关于y的Čech复形得到的双复形，利用该双复形关联的两个谱序列，证明：对所有i,j∈ℕ₀，Extᴿⁱ(R/(x),Hᴵʲ(R))∈S，蕴含对所有j∈ℕ₀，Hᴵʲ(R/(x))∈S。
英文摘要
Let $R$ be a commutative Noetherian ring, let $\mathbf{x}=x_1,\ldots,x_n$ be an $R$-regular sequence, and let $\mathbf{y}=y_1,\ldots,y_m$ be a sequence of elements of $R$. Put $I=(\mathbf y)$. Let $\mathcal S$ be a Serre subcategory of the category of $R$-modules. We consider the double complex obtained from the Koszul co-complex with respect to $\mathbf x$ and the Čech complex with respect to $\mathbf y$. Using the two spectral sequences associated with this double complex, we prove that \[ Ext_R^i(R/(\mathbf x),H_I^j(R))\in\mathcal S \quad\text{for all }i,j\in \mathbb N_0 \] implies \[ H_I^j(R/(\mathbf x))\in\mathcal S \quad\text{for all }j\in\mathbb N_0. \]
CommentsThere were some misprints in some of the formulas in the previous version
