Castelnuovo-Mumford regularity of representations of certain product categories

Liping Li; Wee Liang Gan

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Castelnuovo-Mumford regularity of representations of certain product categories

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arxiv 1903.08317 v3 pith:DUXXSE6I submitted 2019-03-20 math.RT math.KTmath.RA

Wee Liang Gan , Liping Li This is my paper · ORCID

classification math.RTmath.KTmath.RA

keywords categoriesfinitecastelnuovo-mumfordcertainmathrmproductregularityrepresentations

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abstract

We show in this paper that representations of a finite product of categories satisfying certain combinatorial conditions have finite Castelnuovo-Mumford regularity if and only if they are presented in finite degrees, and hence the category consisting of them is abelian. These results apply to examples such as the categories $\mathrm{FI}^m$ and $\mathrm{FI}_G^m$.

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