arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1509.04400math.ACmath.AG
收藏

Tor映射的消失猜想及其派生分裂

The vanishing conjecture for maps of Tor and derived splinters

Linquan Ma

备注：
more details added
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们称一个优良的局部域$(S,n)$满足Tor映射的消失条件，如果对每个具有$A$正则和$A\to R$模有限无挠扩张的$A\to R\to S$，以及每个$A$ -模$M$，映射$Tor^A_i(M, R)\to Tor_i^A(M, S)$对每个$i\geq 1$为零. Hochster-Huneke猜想（等特征定理）因此指出正则环满足这样的消失条件。本文的主要定理表明，在等特征下，满足Tor映射消失条件的环是Bhatt意义下的正导分裂环。特别地，特征$0$中的有理奇点满足消失条件。这大大推广了Hochster-Huneke的结果和Boutot定理。此外，这导致了一个新的（和令人惊讶的）表征有理奇点的分裂模有限扩张。

英文摘要：

We say an excellent local domain $(S,n)$ satisfies the vanishing conditions for maps of Tor, if for every $A\to R\to S$ with $A$ regular and $A\to R$ module-finite torsion-free extension, and every $A$-module $M$, the map $Tor^A_i(M, R)\to Tor_i^A(M, S)$ vanishes for every $i\geq 1$. Hochster-Huneke's conjecture (theorem in equal characteristic) thus states that regular rings satisfy such vanishing conditions. The main theorem of this paper shows that, in equal characteristic, rings that satisfy the vanishing conditions for maps of Tor are exactly derived splinters in the sense of Bhatt. In particular, rational singularities in characteristic $0$ satisfy the vanishing conditions. This greatly generalizes Hochster-Huneke's result and Boutot's theorem. Moreover, this leads to a new (and surprising) characterization of rational singularities in terms of splittings in module-finite extensions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑