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arXiv · 0812.4966

Socle degrees, Resolutions, and Frobenius powers

Andrew R. Kustin·Bernd Ulrich
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Abstract

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 $R/J$.

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Andrew R. Kustin, Bernd Ulrich. 2008-12-29. Socle degrees, Resolutions, and Frobenius powers. https://arxiv.org/abs/0812.4966

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