Socle degrees of Frobenius powers
| dc.creator | Kustin, Andrew R. | |
| dc.creator | Vraciu, Adela N. | |
| dc.date | 2006-06-20 | |
| dc.date.accessioned | 2026-07-07T07:17:30Z | |
| dc.date.available | 2026-07-07T07:17:30Z | |
| dc.description | Let $k$ be a field of positive characteristic $p$, $R$ be a Gorenstein graded $k$-algebra, and $S=R/J$ be an artinian quotient of $R$ by a homogeneous ideal. We ask how the socle degrees of $S$ are related to the socle degrees of $F_R^e(S)=R/J^{[q]}$. If $S$ has finite projective dimension as an $R$-module, then the socles of $S$ and $F_R^e(S)$ have the same dimension and the socle degrees are related by the formula: $$D_i=qd_i-(q-1)a(R),$$ where $$ d_1\le >...\le d_{\ell}\quad\text{and}\quad D_1\le ... \le D_{\ell}$$ are the socle degrees $S$ and $F_R^e(S)$, respectively, and $a(R)$ is the $a$-invariant of the graded ring $R$, as introduced by Goto and Watanabe. We prove the converse when $R$ is a complete intersection. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0606511 | |
| dc.identifier | http://arxiv.org/abs/math/0606511 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113964 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A35 | |
| dc.title | Socle degrees of Frobenius powers | |
| dc.type | text |