D-modules, Bernstein-Sato polynomials and F-invariants of direct summands
We study the structure of D -modules over a ring R which is a direct sum- mand of a polynomial or a power series ring S with coefficients over a field. We relate properties of D -modules over R to D -modules over S . We show that the localization R f and the local cohomology module H i I ( R ) have...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/111072 |
| Acceso en línea: | https://hdl.handle.net/2117/111072 https://dx.doi.org/10.1016/j.aim.2017.09.019 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebraic geometry Commutative algebra Rings (Algebra) D-modules Bernstein–Sato polynomial Direct summands Local cohomology F-jumping numbers Test ideals Anells (Àlgebra) Geometria algebraica Àlgebra commutativa Classificació AMS::14 Algebraic geometry::14F (Co)homology theory Classificació AMS::13 Commutative rings and algebras::13N Differential algebra Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory Classificació AMS::16 Associative rings and algebras::16S Rings and algebras arising under various constructions Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We study the structure of D -modules over a ring R which is a direct sum- mand of a polynomial or a power series ring S with coefficients over a field. We relate properties of D -modules over R to D -modules over S . We show that the localization R f and the local cohomology module H i I ( R ) have finite length as D -modules over R . Furthermore, we show the existence of the Bernstein-Sato polynomial for elements in R . In positive characteristic, we use this relation between D -modules over R and S to show that the set of F -jumping numbers of an ideal I ¿ R is contained in the set of F -jumping numbers of its extension in S . As a consequence, the F -jumping numbers of I in R form a |
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