论文标题
Faltings的歼灭者定理和几乎Cohen-Macaulay戒指
Faltings' annihilator theorem and almost Cohen-Macaulay rings
论文作者
论文摘要
Faltings的《歼灭者定理》是局部共同体学理论的重要结果。最近，Doustimehr和Naghipour概括了Falitings的歼灭者定理。他们证明，如果$ r $是Gorenstein戒指的同构图像，则$ f_ \ Mathfrak {a}^\ Mathfrak {b} {b}（m）_n =λ_\ mathfrak {a}^^\ mathfrak {a}^\ mathfrak {b}（m）_n $，美元\ text {用于所有} t \ in \ mathbb {n} \} $和$λ_\ mathfrak {a}^\ mathfrak {b}（m）_n：= \ iff \ = \ if \ {λ_ R_ \ Mathfrak {P}}（M_ \ Mathfrak {P}）\ Mid \ Mathfrak {p} \ in \ operatoTorname {spec} {r} {r} {r} \ text {with} \ operatoRaneAme {with} \ operatoRnAme {dim} {dim}在本文中，我们研究了$ f_ \ mathfrak {a}^\ mathfrak {b}（m）_n $和$λ_\ mathfrak {a}^\ mathfrak {b}（m）_n _n $，并且证明$ r $几乎是Cohen-Macaaulay Ring，然后证明$ f_ \ mathfrak {a}^\ mathfrak {b}（m）_n \geqλ_\ mathfrak {a}^\ mathfrak {b}（m）_n- \ operatateRonname {cmd} {cmd} {r} {r} $。使用此结果，我们证明，如果$ r $是Cohen-Macaulay环的同构图像，则$ f_ \ Mathfrak {a}^\ Mathfrak {b}（m）_n =λ_\ Mathfrak {A}
Faltings' annihilator theorem is an important result in local cohomology theory. Recently, Doustimehr and Naghipour generalized the Falitings' annihilator theorem. They proved that if $R$ is a homomorphic image of a Gorenstein ring, then $f_\mathfrak{a}^\mathfrak{b}(M)_n = λ_\mathfrak{a}^\mathfrak{b}(M)_n$, where $f_\mathfrak{a}^\mathfrak{b}(M)_n := \inf\{i \in \mathbb{N} \mid \operatorname{dim}{\operatorname{Supp}(\mathfrak{b}^t H_\mathfrak{a}^i(M))} \geq n \text{ for all } t\in \mathbb{N}\}$ and $λ_\mathfrak{a}^\mathfrak{b}(M)_n := \inf\{λ_{\mathfrak{a} R_\mathfrak{p}}^{\mathfrak{b} R_\mathfrak{p}}(M_\mathfrak{p}) \mid \mathfrak{p}\in\operatorname{Spec}{R} \text{ with } \operatorname{dim}{R/\mathfrak{p}} \geq n\}$. In this paper, we study the relation between $f_\mathfrak{a}^\mathfrak{b}(M)_n$ and $λ_\mathfrak{a}^\mathfrak{b}(M)_n$, and prove that if $R$ is an almost Cohen-Macaulay ring, then $f_\mathfrak{a}^\mathfrak{b}(M)_n \geq λ_\mathfrak{a}^\mathfrak{b}(M)_n - \operatorname{cmd}{R}$. Using this result, we prove that if $R$ is a homomorphic image of a Cohen-Macaulay ring, then $f_\mathfrak{a}^\mathfrak{b}(M)_n = λ_\mathfrak{a}^\mathfrak{b}(M)_n$.
