Asymptotic vanishing conditions which force regularity in local rings of prime characteristic
| dc.creator | Aberbach, Ian | |
| dc.creator | Li, Jinjia | |
| dc.date | 2007-10-22 | |
| dc.date.accessioned | 2026-07-07T08:37:46Z | |
| dc.date.available | 2026-07-07T08:37:46Z | |
| dc.description | Let $(R,\m,k)$ be a local (Noetherian) ring of positive prime characteristic $p$ and dimension $d$. Let $G_\dt$ be a minimal resolution of the residue field $k$, and for each $i\ge 0$, let $\gothic t_i(R) = \lim_{e\to \8} {\length(H_i(F^e(G_\dt)))}/{p^{ed}}$. We show that if $\gothic t_i(R) = 0$ for some $i>0$, then $R$ is a regular local ring. Using the same method, we are also able to show that if $R$ is an excellent local domain and $\Tor_i^R(k,R^+) = 0$ for some $i>0$, then $R$ is regular (where $R^+$ is the absolute integral closure of $R$). Both of the two results were previously known only for $i = 1$ or 2 via completely different methods. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/0710.4090 | |
| dc.identifier | http://arxiv.org/abs/0710.4090 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140516 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A35 | |
| dc.title | Asymptotic vanishing conditions which force regularity in local rings of prime characteristic | |
| dc.type | text |