Socle degrees, resolutions, and Frobenius powers
Copyright policy )Socle degrees, resolutions, and Frobenius powers
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 $R/J$.
19 pages
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13A35, Alternating map, Socle degrees, socle degrees, Algebra and Number Theory, 13D02, canonical module, grade three Gorenstein ideal, Grade three Gorenstein ideal, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), 13D02; 13A35, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Canonical module, Maximal Cohen–Macaulay module, Hypersurface ring, second syzygy module, Frobenius power, hypersurface ring, maximal Cohen-Macaulay module, FOS: Mathematics, Second syzygy module, alternating map
13A35, Alternating map, Socle degrees, socle degrees, Algebra and Number Theory, 13D02, canonical module, grade three Gorenstein ideal, Grade three Gorenstein ideal, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), 13D02; 13A35, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Canonical module, Maximal Cohen–Macaulay module, Hypersurface ring, second syzygy module, Frobenius power, hypersurface ring, maximal Cohen-Macaulay module, FOS: Mathematics, Second syzygy module, alternating map
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