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 $R/J$.Comment: 19 page

Kustin, Andrew R.