HOMOLOGICAL DEGREES OF REPRESENTATIONS OF CATEGORIES WITH SHIFT FUNCTORS

作者：Li, Liping^*

来源：Transactions of the American Mathematical Society, 2018, 370(4): 2563-2587.

DOI：10.1090/tran/7041

• FI-MODULES
• STABILITY

Let k be a commutative Noetherian ring and let (C) under bar 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 (c) under bar 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, using the result of Church and Ellenberg [arXiv:1506.01022], we obtain another upper bound for homological degrees of finitely generated FI-modules.

• 出版日期2018-4
• 单位湖南师范大学