分枝离散估值环上代数的奇异轨迹

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-10-21 DOI:10.1112/blms.13174

Nawaj KC

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引用次数: 0

摘要

当k$ k$是一个场时，经典雅可比准则计算一个等维的、有限生成的k$ k$ -代数的奇异轨迹，它是由所谓雅可比矩阵的适当次元生成的理想的闭子集。最近，hochester - jeffries和Saito利用p$ p$ -导数，将这一结果推广到任意混合特征的非分枝离散赋值环上的代数。在这些结果的推动下，本文给出并证明了一类具有混合特征的分枝离散估值环上代数的类似雅可比准则。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Singular loci of algebras over ramified discrete valuation rings

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Singular loci of algebras over ramified discrete valuation rings

When $k$ is a field, the classical Jacobian criterion computes the singular locus of an equidimensional, finitely generated $k$ -algebra as the closed subset of an ideal generated by appropriate minors of the so-called Jacobian matrix. Recently, Hochster-Jeffries and Saito have extended this result for algebras over any unramified discrete valuation ring of mixed characteristic via the use of $p$ -derivations. Motivated by these results, in this paper, we state and prove an analogous Jacobian criterion for algebras over ramified discrete valuation rings of mixed characteristic.