Vanishing of Tor over fiber products

Thiago H. Freitas; Victor Hugo Jorge Pérez; Roger Wiegand; Sylvia Wiegand

Vanishing of Tor over fiber products

Commutative Algebra 2019-09-02 v4

Authors: Thiago H. Freitas , Victor Hugo Jorge Pérez , Roger Wiegand , Sylvia Wiegand

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.

Keywords

local rings fiber product tor vanishing finitely generated modules

Cite

@article{arxiv.1905.09697,
  title  = {Vanishing of Tor over fiber products},
  author = {Thiago H. Freitas and Victor Hugo Jorge Pérez and Roger Wiegand and Sylvia Wiegand},
  journal= {arXiv preprint arXiv:1905.09697},
  year   = {2019}
}

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