Vanishing of Tor over fiber products
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- by T. H. Freitas, V. H. Jorge Pérez, R. Wiegand and S. Wiegand PDF
- Proc. Amer. Math. Soc. 149 (2021), 1817-1825 Request permission
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 Nasseh and Sather-Wagstaff, we explore consequences of the vanishing of $\mathrm {Tor}^R_m(M,N)$ for various values of $m$, where $M$ and $N$ are finitely generated $R$-modules.References
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Additional Information
- T. H. Freitas
- Affiliation: Universidade Tecnológica Federal do Paraná, Departamento de Matemática, 85053-525, Guarapuava-PR, Brazil
- MR Author ID: 1177789
- Email: freitas.thf@gmail.com
- V. H. Jorge Pérez
- Affiliation: Universidade de São Paulo - ICMC - Departamento de Matemática, Caixa Postal 668, 13560-970, São Carlos-SP, Brazil
- Email: vhjperez@icmc.usp.br
- R. Wiegand
- Affiliation: Department of Mathematics, University of Nebraska–Lincoln, Lincoln, Nebraska 68588-0130
- MR Author ID: 205253
- Email: rwiegand@unl.edu
- S. Wiegand
- Affiliation: Department of Mathematics, University of Nebraska–Lincoln, Lincoln, Nebraska 68588-0130
- MR Author ID: 182675
- Email: swiegand1@unl.edu
- Received by editor(s): June 12, 2019
- Received by editor(s) in revised form: August 28, 2019, and September 17, 2019
- Published electronically: March 3, 2021
- Additional Notes: All four authors were partially supported by FAPESP-Brazil 2018/05271-6, 2018/05268-5 and CNPq-Brazil 421440/2016-3. The third author was partially supported by Simons Collaboration Grant 426885. The fourth author was partially supported by a UNL Emeriti & Retiree Association Wisherd Award
- Communicated by: Claudia Polini
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 1817-1825
- MSC (2020): Primary 13D07
- DOI: https://doi.org/10.1090/proc/14907
- MathSciNet review: 4232178