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arXiv · 1905.09697

Vanishing of Tor over fiber products

Thiago H. Freitas·Victor Hugo Jorge Pérez·Roger Wiegand·Sylvia Wiegand
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Abstract

Let $(S,\mathfrak{m},k)$ and $(T,\mathfrak{n},k)$ be local rings, and let $R$ denote their fiber product over their common residue field $k$. Inspired by work of Naseh and Sather-Wagstaff, we explore consequences of vanishing of ${\rm Tor}^R_m(M,N)$ for various values of $m$, where $M$ and $N$ are finitely generated $R$-modules.

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Thiago H. Freitas, Victor Hugo Jorge Pérez, Roger Wiegand, Sylvia Wiegand. 2019-05-23. Vanishing of Tor over fiber products. https://arxiv.org/abs/1905.09697

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