D-modules, Bernstein-Sato polynomials and F-invariants of direct summands
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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
CitationAlvarez, J., Huneke, C., Núñez-Betancourt, L. D-modules, Bernstein-Sato polynomials and F-invariants of direct summands. "Advances in mathematics", 1 Desembre 2017, vol. 321, p. 298-325.