## 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 $M$).## References

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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