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Homological degrees of representations of categories with shift functors

Liping Li

K-Theory and Homology Representation Theory Rings and Algebras mathscidoc:1702.02011

to appear in Trans. Amer. Math. Soc., 2017
Let k be a commutative Noetherian ring and Cāˆ’āˆ’ be a locally finite k-linear category equipped with a self-embedding functor of degree 1. We show under a moderate condition that finitely generated torsion representations of Cāˆ’āˆ’ are super finitely presented (that is, they have projective resolutions each term of which is finitely generated). In the situation that these self-embedding functors are genetic functors, we give upper bounds for homological degrees of finitely generated torsion modules. These results apply to quite a few categories recently appearing in representation stability theory. In particular, when k is a field of characteristic 0, we obtain another upper bound for homological degrees of finitely generated FI-modules.
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@inproceedings{liping2017homological,
  title={Homological degrees of representations of categories with shift functors},
  author={Liping Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170222105803852457502},
  booktitle={to appear in Trans. Amer. Math. Soc.},
  year={2017},
}
Liping Li. Homological degrees of representations of categories with shift functors. 2017. In to appear in Trans. Amer. Math. Soc.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170222105803852457502.
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