\title{Symmetric tensor categories in characteristic 2}

\author{Dave Benson and Pavel Etingof} 

\begin{abstract} 
We construct and study a nested sequence of finite symmetric tensor 
categories $\Vec=\C_0\subset \C_1\subset\cdots\subset \C_n\subset\cdots$
over a field of characteristic $2$ such that $\C_{2n}$ are
incompressible, i.e., do not admit tensor functors into 
tensor categories of smaller Frobenius--Perron dimension. 
This generalizes the category $\C_1$ described by Venkatesh \cite{Ven} and the category $\C_2$ defined by Ostrik. 
The Grothendieck rings of the categories $\C_{2n}$ and $\C_{2n+1}$ are
both isomorphic to the ring of real cyclotomic integers defined by a primitive $2^{n+2}$-th root of unity, 
$\mO_n=\ZZ[2\cos(\pi/2^{n+1})]$. 
\end{abstract}