论文标题
差异模块中的估值和非零扭转
Valuations and Nonzero Torsion in Module of Differentials
论文作者
论文摘要
令$（R，\ Mathfrak {M} _r，K）$为一维完全减少的$ K $ -Algebra，在特征零字段上。 R. Berger猜想$ r $是规则的，并且仅当差速器的普遍有限模块$ω_r$是免费的。当$ r $是一个域时，我们在多种情况下证明了猜想。我们的技术主要依赖于利用$ r $的估值半组。首先，我们通过分析$ r $的估值半组和$ r $的整体关闭单位订单来建立一种验证猜想的方法。我们还证明了在某些单一元素中缺少$ r $的单一支持的情况下的猜想。这些单元基于$ \ mathfrak {m} _r $的最小功率，该功率包含在导体理想中。这也概括了Cortiñas，Geller和Weibel的先前结果。
Let $(R,\mathfrak{m}_R,k)$ be a one-dimensional complete local reduced $k$-algebra over a field of characteristic zero. R. Berger conjectured that $R$ is regular if and only if the universally finite module of differentials $Ω_R$ is torsion free. When $R$ is a domain, we prove the conjecture in several cases. Our techniques are primarily reliant on making use of the valuation semi-group of $R$. First, we establish a method of verifying the conjecture by analyzing the valuation semi-group of $R$ and orders of units of the integral closure of $R$. We also prove the conjecture in the case when certain monomials are missing from the monomial support of the defining ideal of $R$. These monomials are based on the smallest power of $\mathfrak{m}_R$ that is contained within the conductor ideal. This also generalizes a previous result of Cortiñas, Geller and Weibel.
