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Some numerical invariants of local rings

Author: Josep Àlvarez Montaner
Journal: Proc. Amer. Math. Soc. 132 (2004), 981-986
MSC (2000): Primary 13D45, 13N10
Published electronically: November 4, 2003
MathSciNet review: 2045412
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Abstract: Let $R$ 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 $R/I$ 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 $I$, are invariants of $R/I$.

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Additional Information

Josep Àlvarez Montaner
Affiliation: Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Avinguda Diagonal 647, Barcelona 08028, Spain

Keywords: Local cohomology, $\mathcal{D}$-modules
Received by editor(s): September 24, 2002
Received by editor(s) in revised form: December 2, 2002
Published electronically: November 4, 2003
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2003 American Mathematical Society