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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Local cohomology of Rees algebras and Hilbert functions
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by Bernard Johnston and Jugal Verma PDF
Proc. Amer. Math. Soc. 123 (1995), 1-10 Request permission

Abstract:

Let I be an ideal primary to the maximal ideal in a local ring. We utilize two well-known theorems due to J.-P. Serre to prove that the difference between the Hilbert function and the Hilbert polynomial of I is the alternating sum of the graded pieces of the graded local cohomology (with respect to its positively-graded ideal) of the Rees ring of I. This gives new insight into the higher Hilbert coefficients of I. The result is inspired by one due to J. D. Sally in dimension two and is implicit in a paper by D. Kirby and H. A. Mehran, where very different methods are used.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1-10
  • MSC: Primary 13D45; Secondary 13A30, 13D40
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1217453-X
  • MathSciNet review: 1217453