Socle degrees，Resolutions，and Frobenius powers
Socle degrees, Resolutions, and Frobenius powers
摘要：
我们首先描述了一种情况，其中每个分级贝蒂数在尾部的决议$\frac RJ$可以读取从基座度的$\frac RJ$。然后将上述结果应用于理想$J$和$J^{[q]}$，从而描述了$R/J^{[q]}$分解尾部的分次贝蒂数等于$R/J$分解移位尾部的分次贝蒂数的情形.
英文摘要：
We first describe a situation in which every graded Betti number in the tail of the resolution of $\frac RJ$ may be read from the socle degrees of $\frac RJ$. Then we apply the above result to the ideals $J$ and $J^{[q]}$; and thereby describe a situation in which the graded Betti numbers in the tail of the resolution of $R/J^{[q]}$ are equal to the graded Betti numbers in the tail of a shift of the resolution of $R/J$.
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。
