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D-module and F-module length of local cohomology modules
University of Michigan, USA.ORCID iD: 0000-0003-4457-2943
2018 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 370, no 12, p. 8551-8580Article in journal (Refereed) Published
Abstract [en]

Let R be a polynomial or power series ring over a field k. We study the length of local cohomology modules H-I(j) (R) in the category of D-modules and F-modules. We show that the D-module length of H-I(j) (R) is bounded by a polynomial in the degree of the generators of I. In characteristic p > 0 we obtain upper and lower bounds on the F-module length in terms of the dimensions of Frobenius stable parts and the number of special primes of local cohomology modules of R/I. The obtained upper bound is sharp if R/I is an isolated singularity, and the lower bound is sharp when R/I is Gorenstein and F-pure. We also give an example of a local cohomology module that has different D-module and F-module lengths.

Place, publisher, year, edition, pages
2018. Vol. 370, no 12, p. 8551-8580
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:su:diva-164876DOI: 10.1090/tran/7266ISI: 000447549300011OAI: oai:DiVA.org:su-164876DiVA, id: diva2:1280590
Available from: 2019-01-20 Created: 2019-01-20 Last updated: 2019-02-01Bibliographically approved

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Smirnov, Ilya
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