FIG-modules over coherent rings

Stability for Representations of Hecke Algebras of Type A

“…Thus, a sequence of representations of symmetric groups can be described by a functor between categories, that is, an FI-module. Many important results have been obtained, such as homological properties of FI-modules, Noetherian properties, and representation stability properties, in a series of articles [3][4][5][6][7][8].…”

FI-modules over preadditive categories and torsion theories

“…This was further developed by Church, Ellenberg and Farb [10], [11], by Church, Ellenberg, Farb and Nagpal [9], by Church and Ellenberg [12], by Putman [27], by Putman and Sam [28], and by Sam and Snowden [30], [31]. Since then, a wide variety of results on F I-modules has been developed by numerous authors, with applications to algebraic topology, algebraic geometry and representation theory (see, for instance, [13], [22], [23], [25], [29]).…”

$FI$-modules over preadditive categories and torsion theories

“…This was further developed by Church, Ellenberg and Farb [8], [9], by Church, Ellenberg, Farb and Nagpal [7], by Church and Ellenberg [10], by Putman [24], by Putman and Sam [25], and by Sam and Snowden [27] [28]. Since then, a wide variety of results on F I-modules has been developed by numerous authors, with applications to algebraic topology, algebraic geometry and representation theory (see, for instance, [11], [19], [20], [22], [26]). In this paper, our aim is to study torsion theories for F I-modules.…”