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...

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Bibliographic Details
Author: Álvarez Montaner, Josep|||0000-0001-6793-368X
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
Description
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 $R/I$.