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arXiv · 1602.01981

A short proof of a result of Katz and West

Dipankar Ghosh·Tony J. Puthenpurakal
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Abstract

We give a short proof of a result due to Katz and West: Let $R$ be a Noetherian ring and $I_1,\ldots,I_t$ ideals of $R$. Let $M$ and $N$ be finitely generated $R$-modules and $N' \subseteq N$ a submodule. For every fixed $i \ge 0$, the sets $\mathrm{Ass}_R\left( \mathrm{Ext}_R^i(M, N/I_1^{n_1}\cdots I_t^{n_t} N') \right)$ and $\mathrm{Ass}_R\left( \mathrm{Tor}_i^R(M, N/I_1^{n_1}\cdots I_t^{n_t} N') \right)$ are independent of $(n_1,\ldots,n_t)$ for all sufficiently large $n_1,\ldots,n_t$.

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Dipankar Ghosh, Tony J. Puthenpurakal. 2016-02-05. A short proof of a result of Katz and West. https://doi.org/10.1216/jca-2019-11-2-237

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