Katzman, M. orcid.org/0000-0001-7553-3520, Ma, L., Smirnov, I. et al. (1 more author) (2018) D-module and F-module length of local cohomology modules. Transactions of the American Mathematical Society, 370. pp. 8551-8580. ISSN 0002-9947
Abstract
Let R be a polynomial or power series ring over a field k. We study the length of local cohomology modules HjI (R) in the category of D-modules and Fmodules. We show that the D-module length of HjI (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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 American Mathematical Society. This is an author produced version of a paper subsequently published in Transactions of the American Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 27 Apr 2017 09:57 |
Last Modified: | 16 Nov 2018 12:21 |
Published Version: | https://doi.org/10.1090/tran/7266 |
Status: | Published |
Publisher: | American Mathematical Society |
Refereed: | Yes |
Identification Number: | 10.1090/tran/7266 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:115305 |