Seibert, Gerhard (1997) The Hilbert-Kunz function of rings of finite Cohen-Macaulay type. ARCHIV DER MATHEMATIK, 69 (4). pp. 286-296. ISSN 0003-889X, 1420-8938
Full text not available from this repository.Abstract
Let (R, m, k) be a Noetherian local ring of prime characteristic p and d its Krull dimension. It is known that for an m-primary ideal l of R and a finitely generated R-module N the limit lim(n=infinity l?R(N/Gamma?(\n\N)/p(dn) exists where I-[n] denotes the ideal of R generated by x(Pn), x is an element of I, and I-R(M) the length of an R-module M. We will show that the ordinary generating function (n=0)Sigma(infinity)l(R)(N/(IN)-N-\n\)t(n) is an element of Q[[t]] of the Hilbert-Kunz function N --> N, n --> I-R(N/Gamma(\n\)N) is rational, i.e., an element of Q(t), if R-(1) is a finite R-module, N a maximal Cohen-Macaulay module and R is of finite Cohen-Macaulay type, i.e., the number of isomorphism classes of finite, indecomposable maximal Cohen-Macaulay modules over R is finite. From this result, we deduce that lim l(R)(N/I-(N)N)/p(dn) is an element of Q. Here R-(1) denotes R considered as an R-algebra via the Frobenius map R --> R, x --> x(P). Actually we will consider a somewhat more general situation using the Frobenius functor.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FROBENIUS |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Mar 2023 06:44 |
| Last Modified: | 28 Mar 2023 06:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/50491 |
Actions (login required)
 |
View Item |
