论文标题
部分追踪理想和伯杰的猜想
Partial Trace Ideals And Berger's Conjecture
论文作者
论文摘要
对于任何有限生成的模块$ m $，在交换一维的Noetherian本地域中，非零等级，我们根据$ m $的部分跟踪理想研究数值不变的$ \ permatatorname {h}（m）$。我们研究了它的特性，并探讨了导体的不变和结构之间的关系。最后，我们将其应用于普遍有限的差速器模块$ω_{r/k} $，其中$ r $是一个完整的$ k $ - algebra，带有$ k $任何完美的领域，以研究R. W. Berger引起的长期猜想。
For any finitely generated module $M$ with non-zero rank over a commutative one-dimensional Noetherian local domain, we study a numerical invariant $\operatorname{h}(M)$ based on a partial trace ideal of $M$. We study its properties and explore relations between this invariant and the colength of the conductor. Finally we apply this to the universally finite module of differentials $Ω_{R/k}$, where $R$ is a complete $k$-algebra with $k$ any perfect field, to study a long-standing conjecture due to R. W. Berger.
