解析代数和形式代数的关系类型

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-09-18 DOI:10.1016/j.bulsci.2025.103739

Maryam Akhavin, Abbas Nasrollah Nejad

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引用次数: 0

摘要

引入解析和形式k-代数关系类型的概念，将F. Planas-Vilanova的结果推广到仿射k-代数。我们用andr - quillen同调和Jacobi-Zariski长精确同调序列对其进行了刻画，证明了这一概念的确定性和不变性。特别地，我们证明了关系类型是域上有限型格式、解析变型和代数变型的不变量。对某些特殊品种的关系类型进行了讨论和分析。

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The relation type of analytic and formal algebras

We introduce the notion of relation types for analytic and formal k-algebras, extending a result by F. Planas-Vilanova to affine k-algebras. We establish the well-definedness and invariance of this notion by characterizing it in terms of André-Quillen homology and utilizing the Jacobi-Zariski long exact sequence of homology. In particular, we show that the relation type is an invariant of schemes of finite type over a field, analytic varieties, and algebroid varieties. We also provide a discussion and analysis of relation types for certain special varieties.

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