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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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A sub-functor for Ext and Cohen-Macaulay associated graded modules with bounded multiplicity
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by Tony J. Puthenpurakal PDF
Trans. Amer. Math. Soc. 373 (2020), 2567-2589 Request permission

Abstract:

Let $(A,\mathfrak {m})$ be a Cohen-Macaulay local ring and let $\mathrm {CM}(A)$ be the category of maximal Cohen-Macaulay $A$-modules. We construct $T \colon \mathrm {CM}(A)\times \mathrm {CM}(A) \rightarrow \operatorname {mod}(A)$, a subfunctor of $\operatorname {Ext}^1_A(-, -)$ and use it to study properties of associated graded modules over $G(A) = \bigoplus _{n\geq 0} \mathfrak {m}^n/\mathfrak {m}^{n+1}$, the associated graded ring of $A$. As an application we give several examples of complete Cohen-Macaulay local rings $A$ with $G(A)$ Cohen-Macaulay and having distinct indecomposable maximal Cohen-Macaulay modules $M_n$ with $G(M_n)$ Cohen-Macaulay and the set $\{e(M_n)\}$ bounded (here $e(M)$ denotes multiplicity of $M$).
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Additional Information
  • Tony J. Puthenpurakal
  • Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
  • MR Author ID: 715327
  • Email: tputhen@math.iitb.ac.in
  • Received by editor(s): August 21, 2018
  • Received by editor(s) in revised form: June 20, 2019, and August 14, 2019
  • Published electronically: January 23, 2020
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 2567-2589
  • MSC (2010): Primary 13A30, 13C14; Secondary 13D40, 13D07
  • DOI: https://doi.org/10.1090/tran/8012
  • MathSciNet review: 4069228