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arXiv · 1710.05123

Hom and Ext, Revisited

Hailong Dao·Mohammad Eghbali·Justin Lyle
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Abstract

Let $R$ be a commutative Noetherian local ring and $M,N$ be finitely generated $R$-modules. We prove a number of results of the form: if $\mbox{Hom}_R(M,N)$ has some nice properties and $\mbox{Ext}^{1 \leq i \leq n}_R(M,N)=0$ for some $n$, then $M$ (and sometimes $N$) must be be close to free. Our methods are quite elementary, yet they suffice to give a unified treatment, simplify, and sometimes extend a number of results in the literature.

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Hailong Dao, Mohammad Eghbali, Justin Lyle. 2017-11-02. Hom and Ext, Revisited. https://arxiv.org/abs/1710.05123

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