关于Ext模族的有限生成
On the finite generation of a family of Ext modules
摘要：
设$Q$是有限Krull维数的Noether环，$\mathbf{f}= f_1,... f_c$是$Q$中的正则序列.设置$A = Q/(\mathbf{f})$。设$I$是$A$中的理想，$M$是一个具有$\projdim_Q M$有限性的随机生成的$A$ -模.集合$\R = \bigoplus_{n\geq 0}I^n$，$I$的里斯-代数。设$N = \bigoplus_{j \geq 0}N_j$是一个随机生成的分级$\R$ -模.证明了\[\bigoplus_{j\geq 0}\bigoplus_{i\geq 0} \Ext^{i}_{A}(M,N_j) \]是$\Sc = \R[t_1,...,t_c]$上的一个双阶化模.我们给出了两个应用程序的局部完全交环的结果。
英文摘要：
Let $Q$ be a Noetherian ring with finite Krull dimension and let $\mathbf{f}= f_1,... f_c$ be a regular sequence in $Q$. Set $A = Q/(\mathbf{f})$. Let $I$ be an ideal in $A$, and let $M$ be a finitely generated $A$-module with $\projdim_Q M$ finite. Set $\R = \bigoplus_{n\geq 0}I^n$, the Rees-Algebra of $I$. Let $N = \bigoplus_{j \geq 0}N_j$ be a finitely generated graded $\R$-module. We show that \[\bigoplus_{j\geq 0}\bigoplus_{i\geq 0} \Ext^{i}_{A}(M,N_j) \] is a finitely generated bi-graded module over $\Sc = \R[t_1,...,t_c]$. We give two applications of this result to local complete intersection rings.
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