Graded Version of Some Basic Theorems on Local Cohomology to a Pair of Ideals

2015/01/27 by P. H. Lima, Lima, P. H., V. H. Jorge Pérez +1
Computer Science · Mathematics · Medicine · #13D45 #Cholinesterase and Neurodegenerative Diseases #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1501.06766

openalex publication_date 2015/01/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove some well-known results on local cohomology with respect to a pair of ideals in graded version, such as, Independence Theorem, Lichtenbaum-Harshorne Vanishing Theorem, Basic Finiteness and Vanishing Theorem, among others. Besides, we present a generalized version of Melkersson Theorem about Artinianess of modules and a result concerning Artinianess of local cohomology modules.

Related

• Local cohomology based on a nonclosed support defined by a pair of ideals
• On graded local cohomology modules defined by a pair of ideals
• Some results on the local cohomology modules with respect to a pair of ideals
• Some properties of generalized local cohomology modules with respect to a pair of ideals
• Artinianness of local cohomology modules