$p$-adic dimensions in symmetric tensor categories in characteristic $p$

Pavel Etingof, Nate Harman, Victor Ostrik

To every object $X$ of a symmetric tensor category over a field of characteristic $p>0$ we attach $p$-adic integers ${\text{Dim}}_{+}(X)$ and ${\text{Dim}}_{-}(X)$ whose reduction modulo $…