Some numerical invariants of local rings. (English) Zbl 1060.13006
Let \(k\) be a field of characteristic zero and \(I\) an ideal of the formal power series ring \(R= k[[x_1,\dots, x_n]]\). The author proves that the multiplicities of the characteristic cycle of the local cohomology modules \(H^{n-i}_I(R)\) and \(H^p_{\mathfrak p}(H^{n-i}_I(R))\), when \({\mathfrak p}\subseteq R\) is any prime ideal that contains \(I\), are invariants of \(R/I\).
Reviewer: Ali Benhissi (Monastir)
MSC:
| 13D45 | Local cohomology and commutative rings |
| 13N10 | Commutative rings of differential operators and their modules |
| 13F25 | Formal power series rings |
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