Rigidity of Ext and Tor via Flat–Cotorsion Theory

Pub Date : 2023-11-03 DOI:10.1017/s0013091523000573

Lars Winther Christensen, Luigi Ferraro, Peder Thompson

引用次数: 0

Abstract

Abstract Let $\mathfrak{p}$ be a prime ideal in a commutative noetherian ring R and denote by $k(\mathfrak{p})$ the residue field of the local ring $R_\mathfrak{p}$ . We prove that if an R -module M satisfies $\operatorname{Ext}_R^{n}(k(\mathfrak{p}),M)=0$ for some $n\geqslant\dim R$ , then $\operatorname{Ext}_R^i(k(\mathfrak{p}),M)=0$ holds for all $i \geqslant n$ . This improves a result of Christensen, Iyengar and Marley by lowering the bound on n . We also improve existing results on Tor-rigidity. This progress is driven by the existence of minimal semi-flat-cotorsion replacements in the derived category as recently proved by Nakamura and Thompson.

查看原文

微信好友朋友圈 QQ好友复制链接

基于平扭理论的Ext和Tor的刚度

摘要设$\mathfrak{p}$为交换诺瑟环R中的素理想，用$k(\mathfrak{p})$表示局部环$R_\mathfrak{p}$的剩余域。我们证明如果一个R模M对某些$n\geqslant\dim R$满足$\operatorname{Ext}_R^{n}(k(\mathfrak{p}),M)=0$，那么$\operatorname{Ext}_R^i(k(\mathfrak{p}),M)=0$对所有$i \geqslant n$都成立。这通过降低n的界改进了Christensen, Iyengar和Marley的结果。我们还改进了托尔刚度的现有结果。这一进展是由Nakamura和Thompson最近证明的派生类中存在的最小半平扭转替代所推动的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助