Article
Vanishing of Ext and Tor Over Fiber Products
Proceedings of the American Mathematical Society
Document Type
Conference Proceeding
Publication Date
6-22-2017
DOI
10.1090/proc/13633
Disciplines
- Education and
- Mathematics
Abstract
Consider a non-trivial fiber product R=S×kT of local rings S, T with common residue field k. Given two finitely generate R-modules M and N, we show that if TorRi(M,N)=0=TorRi+1(M,N) for some i≥5, then pdR(M)≤1 or pdR(N)≤1. From this, we deduce several consequence, for instance, that R satisfies the Auslander-Reiten Conjecture.
Citation Information
Saeed Nasseh and Sean Sather-Wagstaff. "Vanishing of Ext and Tor Over Fiber Products" Proceedings of the American Mathematical Society Vol. 145 (2017) p. 4661 - 4674 Available at: http://works.bepress.com/saeed_nasseh/34/
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