On Faltings' local-global principle of generalized local cohomology modules

DOI

説明

Let R be a commutative Noetherian ring, I an ideal of R and M, N finitely generated R-modules. Let 0 ≤ n ∈ Z. This note shows that the least integer i such that dim Supp($H^i_I$(M, N)/K) ≥ n for any finitely generated submodule K of $H^i_I$(M, N) equal to the number inf{fI<sub>$\frak{p}$</sub> (M$\frak{p}$,N$\frak{p}$)|$\frak{p}$ ∈ Supp(N/IMN), dim R/$\frak{p}$ ≥ n}, where fI<sub>$\frak{p}$</sub>(M$\frak{p}$,N$\frak{p}$) is the least integer i such that $H^i_{I_{\frak{p}}} (M$\frak{p}$,N$\frak{p}$) is not finitely generated, and IM = ann(M/IM). This extends the main result of Asadollahi-Naghipour [1] and Mehrvarz-Naghipour-Sedghi [8] for generalized local cohomology modules by a short proof.

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詳細情報 詳細情報について

  • CRID
    1390282680252798976
  • NII論文ID
    130005509846
  • DOI
    10.2996/kmj/1490083223
  • ISSN
    18815472
    03865991
  • 本文言語コード
    en
  • データソース種別
    • JaLC
    • Crossref
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用不可

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