Title    : Rational $p$-biset functors
Author   : Serge Bouc
Abstract :
In this paper, I give several characterizations of rational biset functors 
over $p$-groups, which are independent of the knowledge of genetic bases 
for $p$-groups. I~also introduce a construction of new biset functors from 
known ones, which is similar to the Yoneda construction for representable 
functors, and to the Dress construction for Mackey functors, and I show 
that this construction preserves the class of rational $p$-biset functors.

This leads to a characterization of rational $p$-biset functors as additive 
functors from a specific quotient category of the biset category to abelian 
groups. Finally, I give a description of the largest rational quotient of 
the Burnside $p$-biset functor~: when $p$ is odd, this is simply the functor 
$R_\Q$ of rational representations, but when $p=2$, it is a non split extension
of $R_\Q$ by a specific uniserial functor, which happens to be closely related 
to the functor of units of the Burnside ring.