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Generalized Eulerian 𝒟-modules in char p > 0
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-07-24 , DOI: 10.1142/s0219498821501279 Aarti Patle 1 , Jyoti Singh 1
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-07-24 , DOI: 10.1142/s0219498821501279 Aarti Patle 1 , Jyoti Singh 1
Affiliation
Let R be a polynomial ring in n indeterminates with coefficients in the field K of characteristic p > 0 and 𝒟 be the ring of differential operators over R . In this paper, we introduce the notion of generalized Eulerian 𝒟 -modules for characteristic p > 0 and establish their properties. We show that if 𝒯 is any graded Lyubeznik functor on the category of modules over R , then 𝒯 ( R ) is a generalized Eulerian 𝒟 -module. As a consequence, we prove that all socle elements of module H 𝔪 i ( 𝒯 ( R ) ) are concentrated in degree − n , where 𝔪 is an irrelevant maximal ideal of R .
中文翻译:
char p > 0 中的广义欧拉 𝒟 模
让R 是一个多项式环n 与领域中的系数不确定ķ 有特色的p > 0 和𝒟 是微分算子的环R . 在本文中,我们介绍了广义欧拉的概念𝒟 - 特征模块p > 0 并确定它们的属性。我们证明如果𝒯 是模块类别上的任何分级 Lyubeznik 函子R , 然后𝒯 ( R ) 是广义的欧拉𝒟 -模块。因此,我们证明了 module 的所有 socle 元素H 𝔪 一世 ( 𝒯 ( R ) ) 集中在程度 - n , 在哪里𝔪 是一个无关的最大理想R .
更新日期:2020-07-24
中文翻译:
char p > 0 中的广义欧拉 𝒟 模
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