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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Castelnuovo-Mumford regularity of Ext modules and homological degree
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by Marc Chardin, Dao Thanh Ha and Lê Tuân Hoa PDF
Trans. Amer. Math. Soc. 363 (2011), 3439-3456 Request permission

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
  • MR Author ID: 259215
  • 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
  • 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.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3439-3456
  • MSC (2000): Primary 13D45
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05062-2
  • MathSciNet review: 2775813