导出函子与Hilbert多项式
Derived Functors and Hilbert Polynomials
摘要：
设$R$是交换Noether环，$I$是理想，$M$和$N$是交换生成的$R$ -模.设$V(I)\cap Supp(M)\cap Supp(N)$由2个极大理想组成，$ł(\e^i(N/I^nN,M))$表示$\e^i(N/I^nN,M)$的长度。证明了对于$n>>0$，$ł(\e^i(N/I^nN,M))$与$n$中的多项式一致，并给出了其次数的上界.另一方面，一个简单的例子表明，一些特殊的假设，如上述的支持条件是必要的，以得出结论，多项式增长举行。
英文摘要：
Let $R$ be a commutative Noetherian ring, $I$ an ideal, $M$ and $N$ finitely generated $R$-modules. Assume $V(I)\cap Supp(M)\cap Supp(N)$ consists of finitely many maximal ideals and let $ł(\e^i(N/I^nN,M))$ denote the length of $\e^i(N/I^nN,M)$. It is shown that $ł(\e^i(N/I^nN,M))$ agrees with a polynomial in $n$ for $n>>0$, and an upper bound for its degree is given. On the other hand, a simple example shows that some special assumption such as the support condition above is necessary in order to conclude that polynomial growth holds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
