A Rigidity Theorem for Ext

2022/03/03 by Levins, Andrew Soto
#13D07 (Primary) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.01991

Abstract

The goal of this paper is to show that if R is an unramified hypersurface, if M and N are finitely generated R modules, and if Ext_Rⁿ(M,N)=0 for some n\leqgradeM, then Ext_Rⁱ(M,N)=0 for i≤ n. A corollary of this says that Ext_Rⁱ(M,M)≠ 0 for i\leqgradeM and M≠ 0. These results are related to a question of Jorgensen and results of Dao.

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