The monomial conjecture and order ideals II

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• 作者：S.P. Dutta ^{s-dutta@illinois.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 13D02 ; 13D22 ; secondary ; 13C15 ; 13D25 ; 13H05
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：454
• 期：Complete
• 页码：123-138
• 全文大小：393 K

文摘

Let I be an ideal of height d   in a regular local ring (R,m,k=R/m)$(R,m,k=R/m)$ of dimension n   and let Ω denote the canonical module of R/I$R/I$. In this paper we first prove the equivalence of the following: the non-vanishing of the edge homomorhpism ${\eta }_d:{\mathrm{Ext}}_R^{n-d}(k,\mathrm{\Omega })\to {\mathrm{Ext}}_R^n(k,R)$, the validity of the order ideal conjecture for regular local rings, and the validity of the monomial conjecture for all local rings. Next we prove several special cases of the order ideal conjecture/monomial conjecture.