The Artinian first Koszul homology generator conjecture

Let (A,m)(A,m) be an Artinian local ring, and let x1,,xnmx_1,\ldots,x_n\in m. Write H1(x1,,xn;A)H_1(x_1,\ldots,x_n;A) for the first Koszul homology module of the sequence on AA. Artinian Koszul homology conjecture. The module H1(x1,,xn;A)H_1(x_1,\ldots,x_n;A) has at least nn generators as an AA-module. This conjecture is related to the Tor generator conjecture above and is used to study lower bounds for generators of first Koszul homology over Artinian rings. The source provides no resolution status.

Sources & referencesView supporting material

Primary source

Alex Zhongyi Zhang, “The number of generators of the first Koszul homology of an Artinian ring”, arXiv:1411.7096 (2014).

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