论文标题
部分可观测时空混沌系统的无模型预测
Cofiniteness of generalized local cohomology modules for ideals of small dimension
论文作者
论文摘要
令$ \ mathfrak {a} $是通勤的Noetherian环$ r $和$ m，n $ n $两个有限生成的$ r $ modules的理想。通过使用频谱序列参数，可以显示，如果$ \ mathrm {dim} _rm \ leq2 $和$ \ mathrm {h}^{i}^{i} _ \ mathfrak {a} a}（n）$是$ \ mathfrak {a} $ \ mathrm {h}^{i} _ \ mathfrak {a}（n）$是$ \ mathfrak {a} $ - dimension $ \ leq1 $的cofinite模块，每种$ i \ geq1 $ $ \ mathrm {h}^{t} _ \ mathfrak {a}（m，n）$是$ \ mathfrak {a} $ - cofinite- cofinite for All $ t \ geq0 $。
Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$ and $M, N$ two finitely generated $R$-modules. By using a spectral sequence argument, it is shown that if either $\mathrm{dim}_RM\leq2$ and $\mathrm{H}^{i}_\mathfrak{a}(N)$ are $\mathfrak{a}$-cofinite for all $i\geq0$, or $\mathrm{H}^{i}_\mathfrak{a}(N)$ is an $\mathfrak{a}$-cofinite module of dimension $\leq1$ for each $i\geq1$, or $q(\mathfrak{a},R)\leq1$, then the $R$-modules $\mathrm{H}^{t}_\mathfrak{a}(M,N)$ are $\mathfrak{a}$-cofinite for all $t\geq0$.
