Some numerical invariants of local rings
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- by Josep Àlvarez Montaner
- Proc. Amer. Math. Soc. 132 (2004), 981-986
- DOI: https://doi.org/10.1090/S0002-9939-03-07177-6
- Published electronically: November 4, 2003
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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 $R/I$.References
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Bibliographic Information
- Josep Àlvarez Montaner
- Affiliation: Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Avinguda Diagonal 647, Barcelona 08028, Spain
- Email: Josep.Alvarez@upc.es
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 981-986
- MSC (2000): Primary 13D45, 13N10
- DOI: https://doi.org/10.1090/S0002-9939-03-07177-6
- MathSciNet review: 2045412