Some numerical invariants of local rings
Let $R$ be a formal power series ring over a field of characteristic zero and $I\subseteq R$ be any ideal. The aim of this work is to introduce some numerical invariants of the local rings $R/I$ by using theory of algebraic $\mathcal D$-modules. More precisely, we will prove that the multiplicities...
| Author: | |
|---|---|
| Format: | article |
| Publication Date: | 2002 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/834 |
| Online Access: | https://hdl.handle.net/2117/834 |
| Access Level: | Open access |
| Keyword: | Algebra, Homological Differential algebra Local cohomology D-modules Homologia, Teoria d' Àlgebra diferencial Classificació AMS::13 Commutative rings and algebras::13D Homological methods Classificació AMS::13 Commutative rings and algebras::13N Differential algebra |
| Summary: | Let $R$ be a formal power series ring over a field of characteristic zero and $I\subseteq R$ be any ideal. The aim of this work is to introduce some numerical invariants of the local rings $R/I$ by using theory of algebraic $\mathcal D$-modules. More precisely, we will prove that the multiplicities of the characteristic cycle of the local cohomology modules $H_I^{n-i}(R)$ and $H_{\mathfrak{p}}^p(H_I^{n-i}(R))$, where $\mathfrak{p} \subseteq R$ is any prime ideal that contains $I$, are invariants of $R/I$. |
|---|