%0 Journal Article
%T $p$-adic dimensions in symmetric tensor categories in characteristic $p$
%A Pavel Etingof
%A Nate Harman
%A Victor Ostrik
%J Mathematics
%D 2015
%I arXiv
%X 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 $p$ is the categorical dimension $\text{dim}(X)$ of $X$, coinciding with the usual dimension when $X$ is a vector space. We study properties of $\text{Dim}_{\pm}(X)$, and in particular show that they don't always coincide with each other, and can take any value in $\mathbb{Z}_p$. We also discuss the connection of $p$-adic dimensions with the theory of $\lambda$-rings and Brauer characters.
%U http://arxiv.org/abs/1510.04339v2