Mathematics – Commutative Algebra
Scientific paper
2006-06-20
Mathematics
Commutative Algebra
19 pages
Scientific paper
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.
Kustin Andrew R.
Vraciu Adela N.
No associations
LandOfFree
Socle degrees of Frobenius powers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Socle degrees of Frobenius powers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Socle degrees of Frobenius powers will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-621982