The bounded-object conjecture for symmetric tensor categories
Year: 2026
Type: preprint
Abstract: This paper proves the Coulembier–Etingof bounded-object classification conjecture for symmetric tensor categories over algebraically closed fields of arbitrary positive characteristic, without finiteness or projective assumptions. The central construction extends the Frobenius–Perron character of the subcategory generated by the tensor product of a bounded object with its dual to a positive dimension character on the category it generates. In odd characteristic, the proof combines the quadratic Adams operation with a refined cyclotomic argument. In characteristic two, it uses terminating Frobenius descent and dyadic lifting, and determines the Frobenius nilpotence height of every noninvertible bounded object. As a further consequence, categories generated by finitely many bounded objects have uniformly bounded growth dimensions of their simple objects.
Author: Chen, Sihan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223803632