论文标题
分级完整交集的巨大复杂性模块的EXT的渐近行为
Asymptotic behavior of Ext for pairs of modules of large complexity over graded complete intersections
论文作者
论文摘要
让$ m $和$ n $在分级的完整交叉点$ r $上有限生成的分级模块，以便$ \ permatatorName {ext} _r^i（m，n）$具有所有$ i \ gg 0 $的有限长度。我们表明，均匀且奇怪的Hilbert多项式，其长度为$ \ operatatOrname {ext}^i_r（m，n）$，即使是所有大的$ i $，并且所有大的奇数$ $，都具有相同的程度和领先的系数，并且每当这些多项式的最高程度是$ m $ $ $ $或$ n $的最高程度。当$ r $定期进行小型包装时，将给出此结果的改进。
Let $M$ and $N$ be finitely generated graded modules over a graded complete intersection $R$ such that $\operatorname{Ext}_R^i(M,N)$ has finite length for all $i\gg 0$. We show that the even and odd Hilbert polynomials, which give the lengths of $\operatorname{Ext}^i_R(M,N)$ for all large even $i$ and all large odd $i$, have the same degree and leading coefficient whenever the highest degree of these polynomials is at least the dimension of $M$ or $N$. Refinements of this result are given when $R$ is regular in small codimensions.
