D-modules over rings with finite F-representation type
| dc.creator | Takagi, Shunsuke | |
| dc.creator | Takahashi, Ryo | |
| dc.date | 2007-06-26 | |
| dc.date | 2007-12-19 | |
| dc.date.accessioned | 2026-07-07T08:49:58Z | |
| dc.date.available | 2026-07-07T08:49:58Z | |
| dc.description | Smith and Van den Bergh introduced the notion of finite F-representation type as a characteristic $p$ analogue of the notion of finite representation type. In this paper, we prove two finiteness properties of rings with finite F-representation type. The first property states that if $R=\bigoplus_{n \ge 0}R_n$ is a Noetherian graded ring with finite (graded) F-representation type, then for every non-zerodivisor $x \in R$, $R_x$ is generated by $1/x$ as a $D_{R}$-module. The second one states that if $R$ is a Gorenstein ring with finite F-representation type, then $H_I^n(R)$ has only finitely many associated primes for any ideal $I$ of $R$ and any integer $n$. We also include a result on the discreteness of F-jumping exponents of ideals of rings with finite (graded) F-representation type as an appendix. | |
| dc.description | 19 pages; v.2: minor changes, to appear in Math. Res. Lett | |
| dc.identifier | https://arxiv.org/abs/0706.3842 | |
| dc.identifier | http://arxiv.org/abs/0706.3842 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144462 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13A35 (Primary) 13N10, 13D45 (Secondary) | |
| dc.title | D-modules over rings with finite F-representation type | |
| dc.type | text |