Conditions for the Yoneda algebra of a local ring to be generated in low degrees

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• 作者：Justin Hoffmeier^a ; ^{jhoff@nwmissouri.edu" class="auth_mail" title="E-mail the corresponding author} ; Liana M. Şega^b ; ^{segal@umkc.edu" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：221
• 期：2
• 页码：304-315
• 全文大小：359 K

文摘

The powers class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300810&_mathId=si1.gif&_user=111111111&_pii=S0022404916300810&_rdoc=1&_issn=00224049&md5=7ec3cd5551c19f06cef8b51f50e51a17" title="Click to view the MathML source">mⁿclass="mathContainer hidden">class="mathCode">${\mathfrak{m}}^n$ of the maximal ideal class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300810&_mathId=si2.gif&_user=111111111&_pii=S0022404916300810&_rdoc=1&_issn=00224049&md5=eb31d8bae56bde5cf3dd52ba1523008c" title="Click to view the MathML source">mclass="mathContainer hidden">class="mathCode">$\mathfrak{m}$ of a local Noetherian ring R are known to satisfy certain homological properties for large values of n  . For example, the homomorphism class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300810&_mathId=si3.gif&_user=111111111&_pii=S0022404916300810&_rdoc=1&_issn=00224049&md5=d504d69902ea79b71f45d2021c34f4b9" title="Click to view the MathML source">R→R/mⁿclass="mathContainer hidden">class="mathCode">$R\to R/{\mathfrak{m}}^n$ is Golod for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404916300810&_mathId=si4.gif&_user=111111111&_pii=S0022404916300810&_rdoc=1&_issn=00224049&md5=cc68398873f8142b035d16497cb37787" title="Click to view the MathML source">n≫0class="mathContainer hidden">class="mathCode">$n\gg 0$. We study when such properties hold for small values of n, and we make connections with the structure of the Yoneda Ext algebra, and more precisely with the property that the Yoneda algebra of R is generated in degrees 1 and 2. A complete treatment of these properties is pursued in the case of compressed Gorenstein local rings.