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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some numerical invariants of local rings
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by Josep Àlvarez Montaner PDF
Proc. Amer. Math. Soc. 132 (2004), 981-986 Request permission

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
  • 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