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Some numerical invariants of local rings

Authors:	Josep À lvarez Montaner

Institution:	Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Avinguda Diagonal 647, Barcelona 08028, Spain

Abstract:	Let be a formal power series ring over a field of characteristic zero and $I\subseteq R$ any ideal. The aim of this work is to introduce some numerical invariants of the local rings by using the 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 , are invariants of .

Keywords:	Local cohomology $\mathcal{D}$-modules

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