Cohomological Support and the Geometric Join
Cohomological Support and the Geometric Join
复制标题
上同调支持和几何连接
DOI：
10.4171/dm/605
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发表时间：
2016
影响因子：
0.9
通讯作者：
William T. Sanders
中科院分区：
文献类型：
--
作者：
Hailong Dao;William T. Sanders
设$M，N$是局部完全交$R$上的有限生成模。假设对于每个$I&>0$，$\mathm{Tor}^R_i(M，N)=0$。证明了$M_RN$(在Avramov-Buchweitz意义下)的上同调支集等于$M，N$的上同调支集的几何并.这样的结果在两个活跃的领域或研究之间建立了新的联系，并立即产生了几个令人惊讶的推论。当然，它也提出了许多关于完全交上模的同调性质的有趣的新问题，其中一些问题将在本注记的后半部分进行研究。
Let $M,N$ be finitely generated modules over a local complete intersection $R$. Assume that for each $i>0$, $\mathrm{Tor}^R_i(M,N)=0$. We prove that the cohomological support of $M\otimes_R N$ (in the sense of Avramov-Buchweitz) is equal to the geometric join of the cohomological supports of $M,N$. Such result gives a new connection between two active areas or research, and immediately produces several surprising corollaries. Naturally, it also raises many intriguing new questions about the homological properties of modules over a complete intersection, some of those are investigated in the second half of this note.