Mathematics – Commutative Algebra
Scientific paper
2009-04-09
Mathematics
Commutative Algebra
This is to appear in the Mathematische Annalen. (Due to the next work) comments are welcome
Scientific paper
For a Noetherian local domain $R$ let $R^+$ be the absolute integral closure of $R$ and let $R_{\infty}$ be the perfect closure of $R$, when $R$ has prime characteristic. In this paper we investigate the projective dimension of residue rings of certain ideals of $R^+$ and $R_{\infty}$. In particular, we show that any prime ideal of $R_{\infty}$ has a bounded free resolution of countably generated free $R_{\infty}$-modules. Also, we show that the analogue of this result is true for the maximal ideals of $R^+$, when $R$ has residue prime characteristic. We compute global dimensions of $R^+$ and $R_{\infty}$ in some cases. Some applications of these results are given.
No associations
LandOfFree
Homological properties of the perfect and absolute integral closures of Noetherian domains 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 Homological properties of the perfect and absolute integral closures of Noetherian domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homological properties of the perfect and absolute integral closures of Noetherian domains will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-408788