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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Castelnuovo-Mumford regularity of Ext modules and homological degree


Authors: Marc Chardin, Dao Thanh Ha and Lê Tuân Hoa
Journal: Trans. Amer. Math. Soc. 363 (2011), 3439-3456
MSC (2000): Primary 13D45
Published electronically: February 8, 2011
MathSciNet review: 2775813
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Abstract: Bounds for the Castelnuovo-Mumford regularity of Ext modules, over a polynomial ring over a field, are given in terms of the initial degrees, Castelnuovo-Mumford regularities and the number of generators of the two graded modules involved. These general bounds are refined in the case where the second module is the ring. Other estimates, for instance on the size of graded pieces of these modules, are given. We also derive a bound on the homological degree in terms of the Castelnuovo-Mumford regularity. This answers positively a question raised by Vasconcelos.


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Additional Information

Marc Chardin
Affiliation: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4, place Jussieu, F-75005 Paris, France
Email: chardin@math.jussieu.fr

Dao Thanh Ha
Affiliation: Department of Mathematics, University of Vinh, Vietnam
Email: thahanh@yahoo.com

Lê Tuân Hoa
Affiliation: Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam
Email: lthoa@math.ac.vn

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05062-2
PII: S 0002-9947(2011)05062-2
Keywords: Castelnuovo-Mumford regularity, local cohomology, canonical module, deficiency module, homological degree.
Received by editor(s): February 6, 2009
Published electronically: February 8, 2011
Additional Notes: The second and third authors were supported in part by the National Basic Research Program (Vietnam). The third author would also like to thank University of Paris 6 for their financial support and hospitality during his visit in 2007 when this work was started.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.