Decomposition of local cohomology tables of modules with large E-depth
| Autor: | Giulio Caviglia, Alessandro De Stefani |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Polynomial ring Local cohomology Commutative Algebra (math.AC) 01 natural sciences Measure (mathematics) symbols.namesake 0103 physical sciences Decomposition (computer science) FOS: Mathematics 0101 mathematics Mathematics Hilbert series and Hilbert polynomial Algebra and Number Theory Mathematics::Commutative Algebra 010102 general mathematics Mathematics::Rings and Algebras General initial modules Local cohomology tables Revlex-orders Sequentially Cohen-Macaulay modules Mathematics - Commutative Algebra 13D45 Secondary: 13P10 13D07 Cone (topology) symbols Maximal ideal 010307 mathematical physics |
| Popis: | We introduce the notion of E-depth of graded modules over polynomial rings to measure the depth of certain Ext modules. First, we characterize graded modules over polynomial rings with (sufficiently) large E-depth as those modules whose (sufficiently) partial general initial submodules preserve the Hilbert function of local cohomology modules supported at the irrelevant maximal ideal, extending a result of Herzog and Sbarra on sequentially Cohen-Macaulay modules. Second, we describe the cone of local cohomology tables of modules with sufficiently high E-depth, building on previous work of the second author and Smirnov. Finally, we obtain a non-Artinian version of a socle-lemma proved by Kustin and Ulrich. Comment: 23 pages; we corrected some inaccuracies from previous version and performed minor changes |
| Databáze: | OpenAIRE |
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