Cofiniteness of local cohomology modules and subcategories of modules

• Takahashi, Ryo ^[1] ; Wakasugi, Naoki ^[1]
  1. [1] Nagoya University

     Nagoya University

     Naka-ku, Japón

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 76, Fasc. 1, 2025, págs. 1-10
• Idioma: inglés
• DOI: 10.1007/s13348-023-00416-6
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let R be a commutative noetherian ring and I an ideal of R. Assume that for all integers i the local cohomology module {\text {H}}_I^i(R) is I-cofinite. Suppose that R_\mathfrak {p} is a regular local ring for all prime ideals \mathfrak {p} that do not contain I. In this paper, we prove that if the I-cofinite modules form an abelian category, then for all finitely generated R-modules M and all integers i, the local cohomology module {\text {H}}_I^i(M) is I-cofinite.

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